All these tensor examples are from our paper
[A,B]=Ex2_1;
A(:,:,1) =
1 2
3 4
A(:,:,2) =
5 6
7 0
B =
1 0
0 1
Calculate the mode-1 eigenvalues of A. The result is a row vector.
lambda = teneig(A,B,1)
lambda = Columns 1 through 4 0.4105 + 0.0000i -0.4105 + 0.0000i -9.8995 + 0.0000i 9.8995 - 0.0000i Columns 5 through 6 -4.3820 + 0.0000i 4.3820 - 0.0000i
Calculate the mode-2 eigenvalues of A. The result is a row vector.
lambda = teneig(A,B,2)
lambda = Columns 1 through 4 0.2851 + 0.0000i -0.2851 + 0.0000i -9.5652 + 0.0000i 9.5652 - 0.0000i Columns 5 through 6 -4.3536 + 0.0000i 4.3536 - 0.0000i
Calculate the mode-3 eigenvalues of A. The result is a row vector.
lambda = teneig(A,B,3)
lambda = Columns 1 through 4 0.2936 - 0.0000i -0.2936 + 0.0000i -9.4025 + 0.0000i 9.4025 - 0.0000i Columns 5 through 6 -4.3007 + 0.0000i 4.3007 - 0.0000i
[A]=Ex4_1(5)
A(:,:,1) =
-3.0000 -1.5000 -2.3333 -1.7500 -2.2000
-1.5000 0 -0.8333 -0.2500 -0.7000
-2.3333 -0.8333 -1.6667 -1.0833 -1.5333
-1.7500 -0.2500 -1.0833 -0.5000 -0.9500
-2.2000 -0.7000 -1.5333 -0.9500 -1.4000
A(:,:,2) =
-1.5000 0 -0.8333 -0.2500 -0.7000
0 1.5000 0.6667 1.2500 0.8000
-0.8333 0.6667 -0.1667 0.4167 -0.0333
-0.2500 1.2500 0.4167 1.0000 0.5500
-0.7000 0.8000 -0.0333 0.5500 0.1000
A(:,:,3) =
-2.3333 -0.8333 -1.6667 -1.0833 -1.5333
-0.8333 0.6667 -0.1667 0.4167 -0.0333
-1.6667 -0.1667 -1.0000 -0.4167 -0.8667
-1.0833 0.4167 -0.4167 0.1667 -0.2833
-1.5333 -0.0333 -0.8667 -0.2833 -0.7333
A(:,:,4) =
-1.7500 -0.2500 -1.0833 -0.5000 -0.9500
-0.2500 1.2500 0.4167 1.0000 0.5500
-1.0833 0.4167 -0.4167 0.1667 -0.2833
-0.5000 1.0000 0.1667 0.7500 0.3000
-0.9500 0.5500 -0.2833 0.3000 -0.1500
A(:,:,5) =
-2.2000 -0.7000 -1.5333 -0.9500 -1.4000
-0.7000 0.8000 -0.0333 0.5500 0.1000
-1.5333 -0.0333 -0.8667 -0.2833 -0.7333
-0.9500 0.5500 -0.2833 0.3000 -0.1500
-1.4000 0.1000 -0.7333 -0.1500 -0.6000
Calculate the Z-eigenvalues of A.
lambda = zeig(A)
lambda =
Columns 1 through 8
-9.9779 -4.2876 0 0 0 0 0 0
Columns 9 through 16
0 0 0 0 0 0 0 0
Columns 17 through 24
0 0 0 0 0 0 0 0
Columns 25 through 32
0 0 0 0 0 0 0 0
Columns 33 through 40
0 0 0 0 0 0 0 0
Columns 41 through 48
0 0 0 0 0 0 0 0
Columns 49 through 56
0 0 0 0 0 0 0 0
Columns 57 through 62
0 0 0 0 4.2876 9.9779
A = rand(5,5,5)+i*rand(5,5,5);
Calculate the Qi-eigenpairs of A.
[lambda,V] = teig(A); N = length(lambda)
N =
80
Similarly we can compute the Qi-eigenpairs of other random tensors A of different mode and dimension.
A = rand(5,5,5)+i*rand(5,5,5);
Calculate the E-eigenpairs of A.
[lambda,V] = eeig(A); M = length(lambda)
M =
62
Note that M is the number of eigenpairs if choosing m'=2 representatives from each equivalence class. So the number of equivalence classes N in this case should be M/m'=31.
Similarly we can compute the E-eigenpairs of other random tensors A of different mode and dimension.
A = rand(7,7,7)+i*rand(7,7,7); B = rand(7,7,7)+i*rand(7,7,7);
Calculate the B-eigenpairs of A.
[lambda,V] = teig(A,B); N = length(lambda)
N = 448
Similarly we can compute the B-eigenpairs of other random tensors A with A and B having the same mode and dimension.
A = rand(7,7,7)+i*rand(7,7,7); B = rand(7,7)+i*rand(7,7);
Calculate the B-eigenpairs of A.
[lambda,V] = teneig(A,B); M = length(lambda)
M = 254
Note that M is the number of eigenpairs if choosing m'=2 representatives from each equivalence class. So the number of equivalence classes N in this case should be M/m'=127.
Similarly we can compute the B-eigenpairs of other random tensors A with A and B having different mode but the same dimension.
P = Ex5_5()
P =
'z^6+x^4*y^2+x^2*y^4-3*x^2*y^2*z^2'
Calculate the Z-eigenpairs of the symmetric tensor defined by P.
[lambda,V] = zeig(P)
lambda =
Columns 1 through 8
0 0 0 0 0 0 0 0
Columns 9 through 16
0 0 0 0 0 0 0 0
Columns 17 through 24
0 0 0 0 0 0 0 0
Columns 25 through 32
0 0 0 0 0.0156 0.0156 0.0156 0.0156
Columns 33 through 40
0.0156 0.0156 0.0156 0.0156 0.0156 0.0156 0.0156 0.0156
Columns 41 through 48
0.0156 0.0156 0.0156 0.0156 0.2500 0.2500 0.2500 0.2500
Columns 49 through 50
1.0000 1.0000
V =
Columns 1 through 8
-1.0000 1.0000 -1.0000 1.0000 -1.0000 1.0000 -1.0000 1.0000
0 0 0 0 0 0 0 0
-0.0004 0.0004 -0.0004 0.0004 0.0002 -0.0002 0.0001 -0.0001
Columns 9 through 16
-1.0000 1.0000 -0.5774 0.5774 -0.5774 0.5774 -0.5774 0.5774
0 0 -0.5774 0.5774 -0.5774 0.5774 0.5774 -0.5774
0.0004 -0.0004 -0.5774 0.5774 0.5774 -0.5774 -0.5774 0.5774
Columns 17 through 24
0 0 0 0 0 0 0 0
-1.0000 1.0000 -1.0000 1.0000 -1.0000 1.0000 -1.0000 1.0000
-0.0001 0.0001 0.0003 -0.0003 -0.0005 0.0005 0.0003 -0.0003
Columns 25 through 32
0 0 0.5774 -0.5774 0.2623 -0.2623 -0.8253 0.8253
-1.0000 1.0000 -0.5774 0.5774 -0.8253 0.8253 0.2623 -0.2623
-0.0002 0.0002 -0.5774 0.5774 0.5000 -0.5000 -0.5000 0.5000
Columns 33 through 40
-0.8253 0.8253 -0.8253 0.8253 0.2623 -0.2623 -0.8253 0.8253
-0.2623 0.2623 0.2623 -0.2623 -0.8253 0.8253 -0.2623 0.2623
-0.5000 0.5000 0.5000 -0.5000 -0.5000 0.5000 0.5000 -0.5000
Columns 41 through 48
-0.2623 0.2623 -0.2623 0.2623 -0.7071 0.7071 0.7071 -0.7071
-0.8253 0.8253 -0.8253 0.8253 -0.7071 0.7071 -0.7071 0.7071
-0.5000 0.5000 0.5000 -0.5000 0 0 0 0
Columns 49 through 50
0 0
0 0
-1.0000 1.0000
Calculate the H-eigenpairs of the symmetric tensor defined by P.
[lambda,V] = heig(P)
lambda =
Columns 1 through 8
0 0 0 0 0 0 0 0
Columns 9 through 16
0 0 0 0 0 0 0.0555 0.0555
Columns 17 through 24
0.0555 0.0555 0.0555 0.0555 0.0555 0.0555 1.0000 1.0000
Columns 25 through 32
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Columns 33 through 37
1.0000 1.0000 1.0000 1.0000 1.0000
V =
Columns 1 through 8
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0 0 0 0 0 1.0000 1.0000 -1.0000
0.0006 0.0014 -0.0010 0.0003 -0.0012 1.0000 -1.0000 1.0000
Columns 9 through 16
0 0 0 0 0 -1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 -0.4568 0.4568
-0.0002 0.0012 -0.0013 0.0009 -0.0007 1.0000 0.6856 0.6856
Columns 17 through 24
1.0000 0.4568 0.4568 1.0000 -0.4568 -0.4568 1.0000 0.0000
0.4568 1.0000 1.0000 -0.4568 1.0000 1.0000 1.0000 0
-0.6856 0.6856 -0.6856 -0.6856 0.6856 -0.6856 0 1.0000
Columns 25 through 32
0.0015 -0.0014 0 0 0.0000 -0.0000 0.0000 0
0 0 -0.0000 0.0014 0.0000 -0.0000 -0.0000 -0.0014
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Columns 33 through 37
0 0 0.0009 -0.0010 -1.0000
0.0008 -0.0008 0 0 1.0000
1.0000 1.0000 1.0000 1.0000 0
P = Ex5_7(4); % n=4
P =
'(x1-x2)^4+(x1-x3)^4+(x1-x4)^4+(x2-x3)^4+(x2-x4)^4+(x3-x4)^4'
Calculate the Z-eigenvalues of the symmetric tensor defined by P. The result is a row vector.
lambda = zeig(P); distinct_lambda = distinct(lambda)
distinct_lambda =
0 4.0000 5.0000 5.3333
Simply replace n by 5 to 10, we can calculate the Z-eigenvalues of the corresponding tensors defined by P in Example 5.7.
P = ExA_1()
P =
'x1^4+2*x2^4+3*x3^4'
Calculate the Z-eigenpairs of the symmetric tensor defined by P. The result is a row vector.
[lambda,V] = zeig(P)
lambda =
Columns 1 through 8
0.5455 0.5455 0.5455 0.5455 0.5455 0.5455 0.5455 0.5455
Columns 9 through 16
0.6667 0.6667 0.6667 0.6667 0.7500 0.7500 0.7500 0.7500
Columns 17 through 24
1.0000 1.0000 1.2000 1.2000 1.2000 1.2000 2.0000 2.0000
Columns 25 through 26
3.0000 3.0000
V =
Columns 1 through 8
-0.7385 0.7385 0.7385 -0.7385 -0.7385 0.7385 -0.7385 0.7385
0.5222 -0.5222 -0.5222 0.5222 -0.5222 0.5222 -0.5222 0.5222
-0.4264 0.4264 -0.4264 0.4264 0.4264 -0.4264 -0.4264 0.4264
Columns 9 through 16
-0.8165 0.8165 -0.8165 0.8165 -0.8660 0.8660 -0.8660 0.8660
-0.5774 0.5774 0.5774 -0.5774 0 0 0 0
0 0 0 0 0.5000 -0.5000 -0.5000 0.5000
Columns 17 through 24
-1.0000 1.0000 0 0 0 0 0 0
0 0 -0.7746 0.7746 -0.7746 0.7746 -1.0000 1.0000
0 0 0.6325 -0.6325 -0.6325 0.6325 0 0
Columns 25 through 26
0 0
0 0
-1.0000 1.0000
P = ExA_2(2)
Calculate the Z-eigenvalues of the symmetric tensor defined by P. The result is a row vector.
lambda = zeig(P)
lambda =
Columns 1 through 8
-4.0000 -3.0000 -2.0000 -1.2163 -1.0000 -0.9611 -0.8543 -0.6057
Columns 9 through 16
-0.5550 -0.5402 -0.4805 -0.3887 -0.3466 -0.3261 -0.2518 0.2518
Columns 17 through 24
0.3261 0.3466 0.3887 0.4805 0.5402 0.5550 0.6057 0.8543
Columns 25 through 30
0.9611 1.0000 1.2163 2.0000 3.0000 4.0000
P = ExA_3(0) % a = 0
P =
'2*x1^4+3*x2^4+5*x3^4'
Calculate the Z-eigenvalues of the symmetric tensor defined by P. The result is a row vector.
lambda = zeig(P)
lambda =
Columns 1 through 8
0.9677 0.9677 0.9677 0.9677 0.9677 0.9677 0.9677 0.9677
Columns 9 through 16
1.2000 1.2000 1.2000 1.2000 1.4286 1.4286 1.4286 1.4286
Columns 17 through 24
1.8750 1.8750 1.8750 1.8750 2.0000 2.0000 3.0000 3.0000
Columns 25 through 26
5.0000 5.0000
Simply replace a by 0.25, 0.5, 1 or 3, we can calculate the Z-eigenvalues of the corresponding tensors defined by P in Problem 3 of Appendix.
P = ExA_4(-1) % a = -1
P =
'3*x1^4+x2^4+-6*x1^2*x2^2'
Calculate the Z-eigenvalues of the symmetric tensor defined by P. The result is a row vector.
lambda = zeig(P)
lambda = -0.6000 -0.6000 -0.6000 -0.6000 1.0000 1.0000 3.0000 3.0000
Simply replace a by 0, 0.25, 0.5, 2 or 3, we can calculate the Z-eigenvalues of the corresponding tensors defined by P in Problem 4 of Appendix.
A = ExA_5();
Calculate the Z-eigenpairs of the symmetric tensor A.
[lambda,V] = zeig(A,'symmetric')
lambda =
Columns 1 through 8
-1.0954 -1.0954 -0.5629 -0.5629 -0.0451 -0.0451 0.1735 0.1735
Columns 9 through 16
0.2433 0.2433 0.2628 0.2628 0.2682 0.2682 0.3633 0.3633
Columns 17 through 22
0.5105 0.5105 0.8169 0.8169 0.8893 0.8893
V =
Columns 1 through 8
0.5915 -0.5915 -0.1762 0.1762 -0.7797 0.7797 -0.3357 0.3357
-0.7467 0.7467 0.1796 -0.1796 -0.6135 0.6135 -0.9073 0.9073
-0.3043 0.3043 -0.9678 0.9678 -0.1250 0.1250 -0.2531 0.2531
Columns 9 through 16
-0.9895 0.9895 0.1318 -0.1318 -0.6099 0.6099 -0.2676 0.2676
-0.0947 0.0947 -0.4425 0.4425 -0.4362 0.4362 -0.6447 0.6447
0.1088 -0.1088 -0.8870 0.8870 -0.6616 0.6616 -0.7160 0.7160
Columns 17 through 22
0.3598 -0.3598 -0.8412 0.8412 -0.6672 0.6672
-0.7780 0.7780 0.2635 -0.2635 -0.2471 0.2471
0.5150 -0.5150 -0.4722 0.4722 0.7027 -0.7027
A = ExA_6();
Calculate the Z-eigenvalues of the symmetric tensor A.
lambda = zeig(A,'symmetric')
lambda =
Columns 1 through 8
-16.2345 -15.4552 -15.4298 -10.9711 -8.7347 -8.6596 -8.5979 -8.1889
Columns 9 through 16
-7.2165 -6.0000 -5.5674 -5.5668 -5.5218 -5.4817 -5.1402 -4.3358
Columns 17 through 24
-4.2464 -4.0225 -3.9992 3.9992 4.0225 4.2464 4.3358 5.1402
Columns 25 through 32
5.4817 5.5218 5.5668 5.5674 6.0000 7.2165 8.1889 8.5979
Columns 33 through 38
8.6596 8.7347 10.9711 15.4298 15.4552 16.2345
P = ExA_7();
Calculate the Z-eigenpairs of the symmetric tensor defined by P.
[lambda,V] = zeig(P)
lambda =
Columns 1 through 11
-7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000 -7.2000
Columns 12 through 22
-7.2000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000
Columns 23 through 33
-6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000
Columns 34 through 44
-6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -6.0000 -4.5000 -4.5000
Columns 45 through 55
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 56 through 66
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 67 through 77
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 78 through 88
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 89 through 99
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 100 through 110
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 111 through 121
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 122 through 132
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 133 through 143
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 144 through 154
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 155 through 165
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 166 through 176
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 177 through 187
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 188 through 198
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 199 through 209
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 210 through 220
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 221 through 231
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 232 through 242
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000
Columns 243 through 253
-4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.5000 -4.0000 -4.0000 -4.0000
Columns 254 through 264
-4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000
Columns 265 through 275
-4.0000 -4.0000 -4.0000 -4.0000 -4.0000 -4.0000 0 0 0 0 0
Columns 276 through 286
0 0 0 0 0 0 0 0 0 0 0
Columns 287 through 297
0 0 0 0 0 0 0 0 0 0 0
Columns 298 through 308
0 0 0 0 0 0 0 0 0 0 0
Columns 309 through 319
0 0 0 0 0 0 0 0 0 0 0
Columns 320 through 330
0 0 0 0 0 0 0 0 0 0 0
Columns 331 through 341
0 0 0 0 0 0 0 0 0 0 0
Columns 342 through 352
0 0 0 0 0 0 0 0 0 0 0
Columns 353 through 363
0 0 0 0 0 0 0 0 0 0 0
Columns 364 through 374
0 0 0 0 0 0 0 0 0 0 0
Columns 375 through 385
0 0 0 0 0 0 0 0 0 0 0
Columns 386 through 396
0 0 0 0 0 0 0 0 0 0 0
Columns 397 through 407
0 0 0 0 0 0 0 0 0 0 0
Columns 408 through 418
0 0 0 0 0 0 0 0 0 0 0
Columns 419 through 429
0 0 0 0 0 0 0 0 0 0 0
Columns 430 through 440
0 0 0 0 0 0 0 0 0 0 0
Columns 441 through 451
0 0 0 0 0 0 0 0 0 0 0
Columns 452 through 462
0 0 0 0 0 0 0 0 0 0 0
Columns 463 through 473
0 0 0 0 0 0 0 0 0 0 0
Columns 474 through 484
0 0 0 0 0 0 0 0 0 0 0
Columns 485 through 495
0 0 0 0 0 0 0 0 0 0 0
Columns 496 through 506
0 0 0 0 0 0 0 0 0 0 0
Columns 507 through 517
0 0 0 0 0 0 0 0 0 0 0
Columns 518 through 528
0 0 0 0 0 0 0 0 0 0 0
Columns 529 through 539
0 0 0 0 0 0 0 0 0 0 0
Columns 540 through 550
0 0 0 0 0 0 0 0 0 0 0
Columns 551 through 561
0 0 0 0 0 0 0 0 0 0 0
Columns 562 through 572
0 0 0 0 0 0 0 0 0 0 0
Columns 573 through 583
0 0 0 0 0 0 0 0 0 0 0
Columns 584 through 594
0 0 0 0 0 0 0 0 0 0 0
Columns 595 through 605
0 0 0 0 0 0 0 0 0 0 0
Columns 606 through 616
0 0 0 0 0 0 0 0 0 0 0
Columns 617 through 627
0 0 0 0 0 0 0 0 0 0 0
Columns 628 through 638
0 0 0 0 0 0 0 0 0 0 0
Columns 639 through 649
0 0 0 0 0 0 0 0 0 0 0
Columns 650 through 660
0 0 0 0 0 0 0 0 0 0 0
Columns 661 through 671
0 0 0 0 0 0 0 0 0 0 0
Columns 672 through 682
0 0 0 0 0 0 0 0 0 0 0
Columns 683 through 693
0 0 0 0 0 0 0 0 0 0 0
Columns 694 through 704
0 0 0 0 0 0 0 0 0 0 0
Columns 705 through 715
0 0 0 0 0 0 0 0 0 0 0
Columns 716 through 722
0 0 0 0 0 0 0
V =
Columns 1 through 11
0.9129 -0.9129 -0.1826 0.1826 -0.1826 0.1826 0.1826 -0.1826 -0.1826 0.1826 0.1826
-0.1826 0.1826 -0.1826 0.1826 0.9129 -0.9129 0.1826 -0.1826 -0.1826 0.1826 0.1826
-0.1826 0.1826 -0.1826 0.1826 -0.1826 0.1826 0.1826 -0.1826 -0.1826 0.1826 -0.9129
-0.1826 0.1826 -0.1826 0.1826 -0.1826 0.1826 0.1826 -0.1826 0.9129 -0.9129 0.1826
-0.1826 0.1826 0.9129 -0.9129 -0.1826 0.1826 0.1826 -0.1826 -0.1826 0.1826 0.1826
-0.1826 0.1826 -0.1826 0.1826 -0.1826 0.1826 -0.9129 0.9129 -0.1826 0.1826 0.1826
Columns 12 through 22
-0.1826 0 0 0 0 0 0 0 0 0 0
-0.1826 0.7071 -0.7071 0 0 0.7071 -0.7071 0 0 0 0
0.9129 0 0 0 0 0 0 -0.7071 0.7071 0 0
-0.1826 -0.7071 0.7071 0.7071 -0.7071 0 0 0 0 0.7071 -0.7071
-0.1826 0 0 0 0 0 0 0.7071 -0.7071 -0.7071 0.7071
-0.1826 0 0 -0.7071 0.7071 -0.7071 0.7071 0 0 0 0
Columns 23 through 33
0 0 0 0 0.7071 -0.7071 0 0 0.7071 -0.7071 0.7071
0.7071 -0.7071 0 0 0 0 0 0 0 0 -0.7071
0 0 -0.7071 0.7071 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
-0.7071 0.7071 0 0 0 0 0.7071 -0.7071 -0.7071 0.7071 0
0 0 0.7071 -0.7071 -0.7071 0.7071 -0.7071 0.7071 0 0 0
Columns 34 through 44
-0.7071 0 0 0 0 0.7071 -0.7071 0.7071 -0.7071 -0.5562 0.5562
0.7071 0 0 0.7071 -0.7071 0 0 0 0 0.4122 -0.4122
0 -0.7071 0.7071 -0.7071 0.7071 0 0 -0.7071 0.7071 -0.5562 0.5562
0 0.7071 -0.7071 0 0 -0.7071 0.7071 0 0 0.1439 -0.1439
0 0 0 0 0 0 0 0 0 0.4122 -0.4122
0 0 0 0 0 0 0 0 0 0.1439 -0.1439
Columns 45 through 55
0.4263 -0.4263 0.2194 -0.2194 0.1028 -0.1028 -0.2797 0.2797 0.3425 -0.3425 0.0551
0.1240 -0.1240 -0.5722 0.5722 -0.5434 0.5434 0.5773 -0.5773 0.2312 -0.2312 0.4701
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Columns 309 through 319
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-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083
Columns 617 through 627
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083
0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082
Columns 628 through 638
-0.4083 0.4081 -0.4081 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4081 -0.4081 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
Columns 639 through 649
0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082
0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082
Columns 650 through 660
-0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083
-0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
Columns 661 through 671
0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4083 -0.4083 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
Columns 672 through 682
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082
-0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
Columns 683 through 693
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082
0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082
Columns 694 through 704
-0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083
-0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
Columns 705 through 715
0.4083 -0.4083 0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4083 -0.4083 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4083 -0.4083 0.4083
0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4083 -0.4083 0.4082 -0.4082 0.4082
0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4083 -0.4083 0.4082
Columns 716 through 722
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4080 -0.4080
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4085 -0.4085
-0.4083 0.4082 -0.4082 0.4084 -0.4084 0.4082 -0.4082
-0.4082 0.4082 -0.4082 0.4082 -0.4082 0.4085 -0.4085
-0.4082 0.4082 -0.4082 0.4084 -0.4084 0.4080 -0.4080
P = ExA_8()
P =
'(x1+x2+x3+x4)^4+(x2+x3+x4+x5)^4'
Calculate the Z-eigenpairs of the symmetric tensor defined by P.
[lambda,V] = zeig(P);
lambda =
Columns 1 through 11
0 0 0 0 0 0 0 0 0 0 0
Columns 12 through 22
0 0 0 0 0 0 0 0 0 0 0
Columns 23 through 33
0 0 0 0 0 0 0 0 0 0 0
Columns 34 through 44
0 0 0 0 0 0 0 0 0 0 0
Columns 45 through 55
0 0 0 0 0 0 0 0 0 0 0
Columns 56 through 66
0 0 0 0 0 0 0 0 0 0 0
Columns 67 through 77
0 0 0 0 0 0 0 0 0 0 0
Columns 78 through 88
0 0 0 0 0 0 0 0 0 0 0
Columns 89 through 99
0 0 0 0 0 0 0 0 0 0 0
Columns 100 through 110
0 0 0 0 0 0 0 0 0 0 0
Columns 111 through 121
0 0 0 0 0 0 0 0 0 0 0
Columns 122 through 132
0 0 0 0 0 0 0 0 0 0 0
Columns 133 through 143
0 0 0 0 0 0 0 0 0 0 0
Columns 144 through 154
0 0 0 0 0 0 0 0 0 0 0
Columns 155 through 165
0 0 0 0 0 0 0 0 0 0 0
Columns 166 through 176
0 0 0 0 0 0 0 0 0 0 0
Columns 177 through 187
0 0 0 0 0 0 0 0 0 0 0
Columns 188 through 198
0 0 0 0 0 0 0 0 0 0 0
Columns 199 through 209
0 0 0 0 0 0 0 0 0 0 0
Columns 210 through 220
0 0 0 0 0 0 0 0 0 0 0
Columns 221 through 231
0 0 0 0 0 0 0 0 0 0 0
Columns 232 through 238
0 0 0 0.5000 0.5000 24.5000 24.5000
V =
Columns 1 through 11
-0.3557 0.3557 -0.3852 0.3852 -0.3531 0.3531 0.3977 -0.3977 0.0082 -0.0082 -0.0860
0.1818 -0.1818 0.1153 -0.1153 0.0156 -0.0156 -0.5133 0.5133 0.7653 -0.7653 -0.6036
-0.5041 0.5041 -0.4366 0.4366 -0.4201 0.4201 0.5124 -0.5124 -0.1469 0.1469 -0.0929
0.6781 -0.6781 0.7066 -0.7066 0.7576 -0.7576 -0.3968 0.3968 -0.6266 0.6266 0.7825
-0.3557 0.3557 -0.3852 0.3852 -0.3531 0.3531 0.3977 -0.3977 0.0082 -0.0082 -0.0860
Columns 12 through 22
0.0860 -0.2422 0.2422 -0.1210 0.1210 -0.2181 0.2181 -0.2507 0.2507 -0.1973 0.1973
0.6036 -0.2054 0.2054 0.8423 -0.8423 -0.3193 0.3193 0.0786 -0.0786 0.8429 -0.8429
0.0929 -0.3846 0.3846 -0.3377 0.3377 -0.3052 0.3052 -0.5671 0.5671 -0.2820 0.2820
-0.7825 0.8322 -0.8322 -0.3836 0.3836 0.8425 -0.8425 0.7392 -0.7392 -0.3636 0.3636
0.0860 -0.2422 0.2422 -0.1210 0.1210 -0.2181 0.2181 -0.2507 0.2507 -0.1973 0.1973
Columns 23 through 33
-0.0700 0.0700 -0.3930 0.3930 -0.1732 0.1732 -0.2918 0.2918 -0.1499 0.1499 -0.2953
-0.3654 0.3654 0.5064 -0.5064 -0.5065 0.5065 0.8237 -0.8237 -0.3795 0.3795 0.0331
-0.3995 0.3995 -0.5194 0.5194 -0.1359 0.1359 -0.3360 0.3360 -0.3145 0.3145 -0.4975
0.8349 -0.8349 0.4060 -0.4060 0.8155 -0.8155 -0.1960 0.1960 0.8439 -0.8439 0.7596
-0.0700 0.0700 -0.3930 0.3930 -0.1732 0.1732 -0.2918 0.2918 -0.1499 0.1499 -0.2953
Columns 34 through 44
0.2953 -0.0492 0.0492 -0.2814 0.2814 -0.3681 0.3681 -0.3935 0.3935 -0.2565 0.2565
-0.0331 -0.6323 0.6323 0.8148 -0.8148 0.2826 -0.2826 0.4372 -0.4372 0.8193 -0.8193
0.4975 -0.0854 0.0854 -0.4001 0.4001 -0.5254 0.5254 -0.5209 0.5209 -0.1422 0.1422
-0.7596 0.7669 -0.7669 -0.1333 0.1333 0.6109 -0.6109 0.4773 -0.4773 -0.4206 0.4206
0.2953 -0.0492 0.0492 -0.2814 0.2814 -0.3681 0.3681 -0.3935 0.3935 -0.2565 0.2565
Columns 45 through 55
0.3921 -0.3921 0.0278 -0.0278 -0.1404 0.1404 -0.3657 0.3657 -0.3880 0.3880 -0.2119
-0.4953 0.4953 0.4384 -0.4384 0.8354 -0.8354 0.7198 -0.7198 0.4493 -0.4493 -0.0207
0.5216 -0.5216 0.3575 -0.3575 -0.4502 0.4502 -0.4525 0.4525 -0.5283 0.5283 -0.5480
-0.4184 0.4184 -0.8237 0.8237 -0.2450 0.2450 0.0985 -0.0985 0.4670 -0.4670 0.7806
0.3921 -0.3921 0.0278 -0.0278 -0.1403 0.1403 -0.3657 0.3657 -0.3880 0.3880 -0.2119
Columns 56 through 66
0.2119 -0.1235 0.1235 0.1106 -0.1106 -0.3142 0.3142 -0.3440 0.3440 -0.0357 0.0357
0.0207 -0.5819 0.5819 -0.7086 0.7086 0.7597 -0.7597 0.6747 -0.6747 0.8209 -0.8209
0.5480 -0.0844 0.0844 -0.0848 0.0848 -0.4738 0.4738 -0.5213 0.5213 -0.3055 0.3055
-0.7806 0.7898 -0.7898 0.6828 -0.6828 0.0283 -0.0283 0.1906 -0.1906 -0.4798 0.4798
0.2119 -0.1235 0.1235 0.1106 -0.1106 -0.3142 0.3142 -0.3440 0.3440 -0.0357 0.0357
Columns 67 through 77
-0.0889 0.0889 -0.2701 0.2701 0.0876 -0.0876 0.0458 -0.0458 -0.0876 0.0876 0.0738
0.8317 -0.8317 -0.2601 0.2601 -0.6777 0.6777 0.5450 -0.5450 0.7800 -0.7800 -0.8198
-0.2804 0.2804 -0.3031 0.3031 -0.1241 0.1241 0.2167 -0.2167 -0.0848 0.0848 0.2339
-0.4624 0.4624 0.8334 -0.8334 0.7141 -0.7141 -0.8074 0.8074 -0.6075 0.6075 0.5122
-0.0889 0.0889 -0.2701 0.2701 0.0876 -0.0876 0.0458 -0.0458 -0.0877 0.0877 0.0738
Columns 78 through 88
-0.0738 -0.3928 0.3928 -0.2954 0.2954 -0.0390 0.0390 -0.1312 0.1312 -0.2627 0.2627
0.8198 0.7017 -0.7017 0.7195 -0.7195 0.5334 -0.5334 -0.4269 0.4269 0.2201 -0.2201
-0.2339 -0.4295 0.4295 -0.5421 0.5421 0.2961 -0.2961 -0.2811 0.2811 -0.6161 0.6161
-0.5122 0.1206 -0.1206 0.1181 -0.1181 -0.7905 0.7905 0.8392 -0.8392 0.6587 -0.6587
-0.0738 -0.3928 0.3928 -0.2955 0.2955 -0.0390 0.0390 -0.1312 0.1312 -0.2628 0.2628
Columns 89 through 99
-0.3364 0.3364 0.0183 -0.0183 0.1282 -0.1282 -0.0409 0.0409 0.2597 -0.2597 -0.2722
0.8108 -0.8108 0.7624 -0.7624 -0.7379 0.7379 0.5714 -0.5714 -0.7945 0.7945 0.3731
-0.1941 0.1941 -0.1522 0.1522 -0.0391 0.0391 0.2492 -0.2492 0.4805 -0.4805 -0.6452
-0.2802 0.2802 -0.6284 0.6284 0.6489 -0.6489 -0.7797 0.7797 0.0543 -0.0543 0.5444
-0.3364 0.3364 0.0183 -0.0183 0.1282 -0.1282 -0.0409 0.0409 0.2597 -0.2597 -0.2722
Columns 100 through 110
0.2722 -0.0744 0.0744 -0.0737 0.0737 0.0998 -0.0998 0.2329 -0.2329 -0.3338 0.3338
-0.3731 -0.0925 0.0925 -0.2917 0.2917 0.5064 -0.5064 0.6604 -0.6604 0.7900 -0.7900
0.6452 -0.6117 0.6117 -0.4644 0.4644 0.2164 -0.2164 -0.6144 0.6144 -0.3846 0.3846
-0.5444 0.7786 -0.7786 0.8297 -0.8297 -0.8227 0.8227 -0.2790 0.2790 -0.0715 0.0715
0.2722 -0.0744 0.0744 -0.0737 0.0737 0.0998 -0.0998 0.2329 -0.2329 -0.3338 0.3338
Columns 111 through 121
-0.0265 0.0265 0.0294 -0.0294 0.1943 -0.1943 0.4865 -0.4865 0.0128 -0.0128 0.4941
-0.5371 0.5371 0.6622 -0.6622 -0.7066 0.7066 0.3526 -0.3526 0.6762 -0.6762 0.1251
-0.2432 0.2432 0.0546 -0.0546 -0.1273 0.1273 -0.2611 0.2611 0.0460 -0.0460 0.0805
0.8068 -0.8068 -0.7462 0.7462 0.6395 -0.6395 -0.5780 0.5780 -0.7350 0.7350 -0.6997
-0.0265 0.0265 0.0294 -0.0294 0.1943 -0.1943 0.4866 -0.4866 0.0128 -0.0128 0.4941
Columns 122 through 132
-0.4941 0.4410 -0.4410 -0.1686 0.1686 -0.1221 0.1221 0.3055 -0.3055 0.3803 -0.3803
-0.1251 -0.4977 0.4977 0.8424 -0.8424 0.8066 -0.8066 0.0293 -0.0293 -0.1622 0.1622
-0.0805 0.4536 -0.4536 -0.2803 0.2803 -0.1356 0.1356 0.4476 -0.4476 0.4656 -0.4656
0.6997 -0.3969 0.3969 -0.3935 0.3935 -0.5489 0.5489 -0.7824 0.7824 -0.6838 0.6838
-0.4941 0.4410 -0.4410 -0.1686 0.1686 -0.1221 0.1221 0.3055 -0.3055 0.3804 -0.3804
Columns 133 through 143
0.1588 -0.1588 0.2625 -0.2625 0.4302 -0.4302 0.0417 -0.0417 0.2446 -0.2446 -0.0513
-0.5565 0.5565 -0.7632 0.7632 -0.4639 0.4639 -0.7243 0.7243 0.1499 -0.1499 0.7014
-0.3307 0.3307 -0.0275 0.0275 0.4718 -0.4718 -0.0042 0.0042 0.4273 -0.4273 0.0566
0.7284 -0.7284 0.5282 -0.5282 -0.4381 0.4381 0.6869 -0.6869 -0.8218 0.8218 -0.7068
0.1588 -0.1588 0.2625 -0.2625 0.4302 -0.4302 0.0417 -0.0417 0.2446 -0.2446 -0.0513
Columns 144 through 154
0.0513 0.2668 -0.2668 0.5406 -0.5406 0.4426 -0.4426 0.2504 -0.2504 -0.3613 0.3613
-0.7014 0.2624 -0.2624 -0.6280 0.6280 -0.7387 0.7387 0.1593 -0.1593 0.7151 -0.7151
-0.0566 0.3049 -0.3049 0.1368 -0.1368 0.2444 -0.2444 0.4137 -0.4137 -0.4641 0.4641
0.7068 -0.8341 0.8341 -0.0493 0.0493 0.0517 -0.0517 -0.8234 0.8234 0.1103 -0.1103
0.0513 0.2668 -0.2668 0.5406 -0.5406 0.4426 -0.4426 0.2504 -0.2504 -0.3613 0.3613
Columns 155 through 165
0.4599 -0.4599 0.3605 -0.3605 0.3220 -0.3220 -0.0640 0.0640 0.4298 -0.4298 -0.0326
0.0161 -0.0161 0.2275 -0.2275 0.0956 -0.0956 -0.4801 0.4801 -0.5270 0.5270 -0.4388
0.2434 -0.2434 0.2137 -0.2137 0.3813 -0.3813 -0.2817 0.2817 0.4657 -0.4657 -0.3535
-0.7194 0.7194 -0.8017 0.8017 -0.7989 0.7989 0.8258 -0.8258 -0.3685 0.3685 0.8248
0.4599 -0.4599 0.3605 -0.3605 0.3220 -0.3220 -0.0640 0.0640 0.4298 -0.4298 -0.0325
Columns 166 through 176
0.0326 0.4583 -0.4583 0.3848 -0.3848 0.3660 -0.3660 0.3465 -0.3465 0.4471 -0.4471
0.4388 -0.7267 0.7267 -0.7795 0.7795 -0.7826 0.7826 -0.8027 0.8027 -0.4400 0.4400
0.3535 0.2230 -0.2230 0.2933 -0.2933 0.0801 -0.0801 0.3039 -0.3039 0.4474 -0.4474
-0.8248 0.0453 -0.0453 0.1014 -0.1014 0.3365 -0.3365 0.1523 -0.1523 -0.4544 0.4544
0.0325 0.4583 -0.4583 0.3848 -0.3848 0.3660 -0.3660 0.3465 -0.3465 0.4471 -0.4471
Columns 177 through 187
0.1087 -0.1087 0.4137 -0.4137 0.2978 -0.2978 0.3497 -0.3497 -0.0479 0.0479 0.4181
-0.7739 0.7739 -0.1913 0.1913 0.2970 -0.2970 -0.0755 0.0755 -0.7526 0.7526 -0.2115
0.0531 -0.0531 0.4348 -0.4348 0.2305 -0.2305 0.4596 -0.4596 0.1671 -0.1671 0.4372
0.6121 -0.6121 -0.6573 0.6573 -0.8254 0.8254 -0.7338 0.7338 0.6334 -0.6334 -0.6438
0.1087 -0.1087 0.4137 -0.4137 0.2978 -0.2978 0.3497 -0.3497 -0.0479 0.0479 0.4181
Columns 188 through 198
-0.4181 0.3153 -0.3153 -0.0612 0.0612 0.4157 -0.4157 0.2844 -0.2844 0.2251 -0.2251
0.2115 0.0760 -0.0760 0.8113 -0.8113 -0.4225 0.4225 -0.8286 0.8286 0.3487 -0.3487
-0.4372 0.4038 -0.4038 -0.2122 0.2122 0.4912 -0.4912 0.3144 -0.3144 0.2665 -0.2665
0.6438 -0.7952 0.7952 -0.5379 0.5379 -0.4844 0.4844 0.2299 -0.2299 -0.8403 0.8403
-0.4181 0.3153 -0.3153 -0.0611 0.0611 0.4157 -0.4157 0.2844 -0.2844 0.2251 -0.2251
Columns 199 through 209
0.4272 -0.4272 0.3196 -0.3196 0.1710 -0.1710 -0.3601 0.3601 0.2955 -0.2955 0.4189
-0.7144 0.7144 -0.0503 0.0503 0.3801 -0.3801 0.6642 -0.6642 0.2735 -0.2735 -0.3573
0.3478 -0.3478 0.4805 -0.4805 0.2925 -0.2925 -0.5078 0.5078 0.2581 -0.2581 0.4788
-0.0606 0.0606 -0.7498 0.7498 -0.8435 0.8435 0.2037 -0.2037 -0.8270 0.8270 -0.5405
0.4272 -0.4272 0.3196 -0.3196 0.1710 -0.1710 -0.3601 0.3601 0.2955 -0.2955 0.4189
Columns 210 through 220
-0.4189 0.3695 -0.3695 0.3639 -0.3639 0.4033 -0.4033 0.4190 -0.4190 0.3581 -0.3581
0.3573 -0.0406 0.0406 -0.7737 0.7737 -0.2105 0.2105 -0.3217 0.3217 -0.7912 0.7912
-0.4788 0.4148 -0.4148 0.0428 -0.0428 0.4566 -0.4566 0.4713 -0.4713 0.1075 -0.1075
0.5405 -0.7438 0.7438 0.3670 -0.3670 -0.6495 0.6495 -0.5686 0.5686 0.3255 -0.3255
-0.4189 0.3695 -0.3695 0.3639 -0.3639 0.4033 -0.4033 0.4190 -0.4190 0.3581 -0.3581
Columns 221 through 231
0.4170 -0.4170 0.3585 -0.3585 0.3479 -0.3479 0.3808 -0.3808 0.3330 -0.3330 0.2804
-0.3039 0.3039 -0.1029 0.1029 -0.1563 0.1563 -0.7238 0.7238 -0.0080 0.0080 -0.8040
0.4695 -0.4695 0.4637 -0.4637 0.5022 -0.5022 0.4239 -0.4239 0.4397 -0.4397 0.4339
-0.5826 0.5826 -0.7193 0.7193 -0.6938 0.6938 -0.0809 0.0809 -0.7647 0.7647 0.0897
0.4170 -0.4170 0.3585 -0.3585 0.3479 -0.3479 0.3808 -0.3808 0.3330 -0.3330 0.2804
Columns 232 through 238
-0.2804 0.3870 -0.3870 -0.7071 0.7071 -0.2673 0.2673
0.8040 -0.1537 0.1537 0 0 -0.5345 0.5345
-0.4339 0.4532 -0.4532 0 0 -0.5345 0.5345
-0.0897 -0.6866 0.6866 0 0 -0.5345 0.5345
-0.2804 0.3870 -0.3870 0.7071 -0.7071 -0.2673 0.2673
P = ExA_9()
P =
'2*x1^3+3*x1*x2^2+3*x1*x3^2'
Calculate the Z-eigenpairs of the symmetric tensor defined by P.
[lambda,V] = zeig(P)
lambda =
Columns 1 through 11
-2.0000 -2.0000 -2.0000 -2.0000 -2.0000 -2.0000 -2.0000 2.0000 2.0000 2.0000 2.0000
Columns 12 through 14
2.0000 2.0000 2.0000
V =
Columns 1 through 11
-1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 1.0000 1.0000 1.0000 1.0000
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000
-0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000
Columns 12 through 14
1.0000 1.0000 1.0000
0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000
[A]=ExA_10(5);
Calculate the Z-eigenpairs of the tensor A.
[lambda,V] = zeig(A)
lambda =
Columns 1 through 11
-8.8463 -8.8463 -3.9204 -3.9204 0 0 0 0 0 0 0
Columns 12 through 22
0 0 0 0 0 0 0 0 0 0 0
Columns 23 through 33
0 0 0 0 0 0 0 0 0 0 0
Columns 34 through 44
0 0 0 0 0 0 0 0 0 0 0
Columns 45 through 55
0 0 0 0 0 0 0 0 0 0 0
Columns 56 through 66
0 0 0 0 0 0 0 0 0 0 0
Columns 67 through 77
0 0 0 0 0 0 0 0 0 0 0
Columns 78 through 88
0 0 0 0 0 0 0 0 0 0 0
Columns 89 through 99
0 0 0 0 0 0 0 0 0 0 0
Columns 100 through 110
0 0 0 0 0 0 0 0 0 0 0
Columns 111 through 121
0 0 0 0 0 0 0 0 0 0 0
Columns 122 through 132
0 0 0 0 0 0 0 0 0 0 0
Columns 133 through 143
0 0 0 0 0 0 0 0 0 0 0
Columns 144 through 154
0 0 0 0 0 0 0 0 0 0 0
Columns 155 through 165
0 0 0 0 0 0 0 0 0 0 0
Columns 166 through 176
0 0 0 0 0 0 0 0 0 0 0
Columns 177 through 187
0 0 0 0 0 0 0 0 0 0 0
Columns 188 through 198
0 0 0 0 0 0 0 0 0 0 0
Columns 199 through 209
0 0 0 0 0 0 0 0 0 0 0
Columns 210 through 220
0 0 0 0 0 0 0 0 0 0 0
Columns 221 through 231
0 0 0 0 0 0 0 0 0 0 0
Columns 232 through 242
0 0 0 0 0 0 0 4.6408 4.6408 7.2595 7.2595
V =
Columns 1 through 11
0.5809 -0.5809 0.1785 -0.1785 0.1342 -0.1342 -0.5605 0.5605 -0.5085 0.5085 -0.2668
0.3563 -0.3563 -0.4847 0.4847 -0.3929 0.3929 0.6646 -0.6646 0.2023 -0.2023 0.5557
-0.1959 0.1959 -0.7023 0.7023 -0.2948 0.2948 -0.4176 0.4176 -0.6378 0.6378 0.0941
-0.5680 0.5680 -0.2742 0.2742 0.5052 -0.5052 -0.1643 0.1643 0.1980 -0.1980 -0.4348
-0.4179 0.4179 0.4060 -0.4060 -0.6968 0.6968 0.2066 -0.2066 -0.5045 0.5045 0.6498
Columns 12 through 22
0.2668 -0.5231 0.5231 -0.4872 0.4872 -0.6925 0.6925 -0.5686 0.5686 -0.4027 0.4027
-0.5557 0.5969 -0.5969 0.6590 -0.6590 0.5245 -0.5245 0.6248 -0.6248 0.7471 -0.7471
-0.0941 -0.6015 0.6015 -0.2065 0.2065 -0.3412 0.3412 -0.2553 0.2553 -0.3800 0.3800
0.4348 0.0795 -0.0795 -0.3255 0.3255 -0.3421 0.3421 -0.3403 0.3403 -0.0768 0.0768
-0.6498 -0.0443 0.0443 0.4239 -0.4239 0.1095 -0.1095 0.3245 -0.3245 0.3597 -0.3597
Columns 23 through 33
-0.1639 0.1639 -0.3563 0.3563 -0.0080 0.0080 -0.6287 0.6287 -0.2705 0.2705 -0.6668
0.3506 -0.3506 0.7617 -0.7617 -0.1779 0.1779 0.6049 -0.6049 0.3419 -0.3419 0.5089
0.3176 -0.3176 -0.3786 0.3786 -0.4774 0.4774 -0.4238 0.4238 0.2809 -0.2809 -0.2198
-0.5494 0.5494 -0.0391 0.0391 0.5386 -0.5386 -0.2089 0.2089 -0.6041 0.6041 -0.4476
0.6689 -0.6689 0.3848 -0.3848 -0.6710 0.6710 0.1245 -0.1245 0.6050 -0.6050 0.2183
Columns 34 through 44
0.6668 -0.6046 0.6046 -0.4128 0.4128 -0.4238 0.4238 -0.5128 0.5128 -0.2834 0.2834
-0.5089 0.1391 -0.1391 0.7323 -0.7323 0.3366 -0.3366 0.6940 -0.6940 0.6787 -0.6787
0.2198 -0.5771 0.5771 -0.3063 0.3063 0.1989 -0.1989 -0.4453 0.4453 -0.6082 0.6082
0.4476 0.0565 -0.0565 -0.1631 0.1631 -0.6526 0.6526 -0.0963 0.0963 0.2885 -0.2885
-0.2183 -0.5282 0.5282 0.4158 -0.4158 0.4916 -0.4916 0.2186 -0.2186 0.0777 -0.0777
Columns 45 through 55
-0.4951 0.4951 -0.7318 0.7318 -0.7725 0.7725 -0.2108 0.2108 -0.5935 0.5935 -0.2677
0.6939 -0.6939 0.3719 -0.3719 0.3336 -0.3336 0.7309 -0.7309 0.0464 -0.0464 0.5600
-0.3122 0.3122 -0.4951 0.4951 -0.4043 0.4043 -0.1413 0.1413 0.2037 -0.2037 0.0888
-0.2243 0.2243 -0.1854 0.1854 -0.3138 0.3138 -0.1594 0.1594 -0.7617 0.7617 -0.4307
0.3546 -0.3546 -0.2159 0.2159 -0.1734 0.1734 0.6132 -0.6132 0.1543 -0.1543 0.6491
Columns 56 through 66
0.2677 -0.1307 0.1307 -0.4170 0.4170 -0.2295 0.2295 -0.1867 0.1867 -0.3550 0.3550
-0.5600 0.7825 -0.7825 0.7026 -0.7026 0.7469 -0.7469 0.7102 -0.7102 0.2518 -0.2518
-0.0888 -0.3925 0.3925 -0.5503 0.5503 -0.5240 0.5240 -0.0905 0.0905 0.2960 -0.2960
0.4307 0.1753 -0.1753 0.1017 -0.1017 0.2345 -0.2345 -0.1891 0.1891 -0.6814 0.6814
-0.6491 0.4312 -0.4312 0.1389 -0.1389 0.2446 -0.2446 0.6456 -0.6456 0.5086 -0.5086
Columns 67 through 77
-0.7829 0.7829 0.0569 -0.0569 -0.1234 0.1234 0.2014 -0.2014 0.3559 -0.3559 -0.7264
0.0084 -0.0084 0.7491 -0.7491 0.3365 -0.3365 0.6487 -0.6487 -0.1511 0.1511 0.0061
-0.2357 0.2357 -0.3523 0.3523 -0.6718 0.6718 -0.0051 0.0051 -0.3496 0.3496 0.0244
-0.4509 0.4509 0.3062 -0.3062 0.5586 -0.5586 0.0778 -0.0778 0.7232 -0.7232 -0.6808
-0.3579 0.3579 0.4667 -0.4667 -0.3290 0.3290 0.7297 -0.7297 -0.4531 0.4531 -0.0908
Columns 78 through 88
0.7264 -0.5369 0.5369 -0.1174 0.1174 -0.3690 0.3690 0.2172 -0.2172 -0.7494 0.7494
-0.0061 0.3792 -0.3792 0.3188 -0.3188 0.0366 -0.0366 0.1079 -0.1079 0.1767 -0.1767
-0.0244 0.0805 -0.0805 -0.6692 0.6692 0.3895 -0.3895 0.5412 -0.5412 -0.0636 0.0636
0.6808 -0.6335 0.6335 0.5641 -0.5641 -0.7589 0.7589 -0.4076 0.4076 -0.6349 0.6349
0.0908 0.4002 -0.4002 -0.3444 0.3444 0.3672 -0.3672 0.6943 -0.6943 0.0017 -0.0017
Columns 89 through 99
0.4055 -0.4055 -0.0942 0.0942 -0.7151 0.7151 -0.3160 0.3160 -0.0942 0.0942 0.0493
0.3292 -0.3292 0.5793 -0.5793 -0.1023 0.1023 0.7585 -0.7585 0.7807 -0.7807 0.6800
0.3506 -0.3506 0.1246 -0.1246 -0.3148 0.3148 -0.4812 0.4812 -0.3746 0.3746 -0.5030
-0.0693 0.0693 -0.3165 0.3165 -0.2858 0.2858 0.1086 -0.1086 0.1891 -0.1891 0.4738
0.7743 -0.7743 0.7348 -0.7348 -0.5453 0.5453 0.2854 -0.2854 0.4533 -0.4533 0.2401
Columns 100 through 110
-0.0493 -0.3388 0.3388 -0.4013 0.4013 0.5244 -0.5244 -0.0064 0.0064 0.0793 -0.0793
-0.6800 0.7353 -0.7353 0.7188 -0.7188 0.4275 -0.4275 -0.1573 0.1573 -0.3005 0.3005
0.5030 -0.5294 0.5294 -0.2455 0.2455 -0.2003 0.2003 0.6108 -0.6108 -0.3792 0.3792
-0.4738 0.1441 -0.1441 -0.2163 0.2163 0.6164 -0.6164 -0.6394 0.6394 0.5315 -0.5315
-0.2401 0.2083 -0.2083 0.4640 -0.4640 0.3496 -0.3496 0.4397 -0.4397 -0.6907 0.6907
Columns 111 through 121
-0.6561 0.6561 0.1610 -0.1610 0.0425 -0.0425 -0.6365 0.6365 0.0963 -0.0963 0.7655
0.1211 -0.1211 0.4122 -0.4122 0.7524 -0.7524 0.0629 -0.0629 0.5976 -0.5976 -0.0772
0.1070 -0.1070 0.3203 -0.3203 -0.2178 0.2178 -0.5237 0.5237 -0.5411 0.5411 0.0717
-0.7260 0.7260 -0.2705 0.2705 0.1473 -0.1473 -0.0171 0.0171 0.5711 -0.5711 0.6239
0.1278 -0.1278 0.7927 -0.7927 0.6024 -0.6024 -0.5625 0.5625 0.1208 -0.1208 0.1167
Columns 122 through 132
-0.7655 0.3381 -0.3381 0.5209 -0.5209 -0.0775 0.0775 0.3595 -0.3595 0.3369 -0.3369
0.0772 0.5336 -0.5336 0.4547 -0.4547 -0.2933 0.2933 0.5664 -0.5664 0.5927 -0.5927
-0.0717 0.1275 -0.1275 -0.1624 0.1624 0.6086 -0.6086 -0.3146 0.3146 -0.3093 0.3093
-0.6239 0.0768 -0.0768 0.5677 -0.5677 -0.6782 0.6782 0.5683 -0.5683 0.5378 -0.5378
-0.1167 0.7608 -0.7608 0.4162 -0.4162 0.2787 -0.2787 0.3578 -0.3578 0.3877 -0.3877
Columns 133 through 143
0.7490 -0.7490 -0.6938 0.6938 0.6513 -0.6513 -0.0771 0.0771 0.6502 -0.6502 -0.1043
-0.1250 0.1250 0.0642 -0.0642 0.1801 -0.1801 0.7566 -0.7566 0.2937 -0.2937 0.0593
0.4371 -0.4371 -0.4759 0.4759 -0.1381 0.1381 -0.4608 0.4608 -0.0488 0.0488 0.5063
0.2223 -0.2223 -0.1205 0.1205 0.7049 -0.7049 0.3018 -0.3018 0.5883 -0.5883 -0.6508
0.4277 -0.4277 -0.5229 0.5229 0.1657 -0.1657 0.3438 -0.3438 0.3776 -0.3776 0.5529
Columns 144 through 154
0.1043 0.6413 -0.6413 -0.0698 0.0698 -0.3008 0.3008 -0.2385 0.2385 0.6397 -0.6397
-0.0593 0.2725 -0.2725 -0.4458 0.4458 0.7482 -0.7482 -0.2838 0.2838 0.2858 -0.2858
-0.5063 0.2134 -0.2134 -0.2874 0.2874 -0.5146 0.5146 0.5303 -0.5303 0.1921 -0.1921
0.6508 0.3005 -0.3005 0.3225 -0.3225 0.1601 -0.1601 -0.7400 0.7400 0.3198 -0.3198
-0.5529 0.6154 -0.6154 -0.7809 0.7809 0.2434 -0.2434 0.1836 -0.1836 0.6082 -0.6082
Columns 155 through 165
0.5572 -0.5572 0.6883 -0.6883 0.6805 -0.6805 0.2819 -0.2819 0.2445 -0.2445 -0.0885
0.4208 -0.4208 0.2408 -0.2408 -0.0323 0.0323 0.6582 -0.6582 -0.3693 0.3693 0.7279
-0.1214 0.1214 0.0173 -0.0173 -0.0994 0.0994 -0.2359 0.2359 0.6908 -0.6908 -0.1057
0.5618 -0.5618 0.5600 -0.5600 0.7249 -0.7249 0.3981 -0.3981 -0.4647 0.4647 -0.0875
0.4267 -0.4267 0.3929 -0.3929 -0.0202 0.0202 0.5227 -0.5227 0.3327 -0.3327 0.6660
Columns 166 through 176
0.0885 0.4298 -0.4298 -0.2812 0.2812 0.2416 -0.2416 0.6107 -0.6107 0.0346 -0.0346
-0.7279 0.5304 -0.5304 -0.4925 0.4925 0.6579 -0.6579 -0.1086 0.1086 0.6440 -0.6440
0.1057 -0.2422 0.2422 0.4633 -0.4633 -0.3388 0.3388 -0.1648 0.1648 0.0496 -0.0496
0.0875 0.5593 -0.5593 -0.6710 0.6710 0.4730 -0.4730 0.7455 -0.7455 -0.1305 0.1305
-0.6660 0.4031 -0.4031 -0.1161 0.1161 0.4127 -0.4127 -0.1797 0.1797 0.7514 -0.7514
Columns 177 through 187
-0.1856 0.1856 0.6718 -0.6718 0.6746 -0.6746 0.6960 -0.6960 0.6281 -0.6281 0.3285
0.7618 -0.7618 0.2785 -0.2785 -0.4465 0.4465 -0.0394 0.0394 0.3048 -0.3048 0.5437
-0.4886 0.4886 0.0712 -0.0712 0.1461 -0.1461 0.4593 -0.4593 0.1804 -0.1804 -0.3833
0.2333 -0.2333 0.4806 -0.4806 0.5237 -0.5237 0.1362 -0.1362 0.3189 -0.3189 0.6184
0.3035 -0.3035 0.4848 -0.4848 -0.2232 0.2232 0.5334 -0.5334 0.6151 -0.6151 0.2593
Columns 188 through 198
-0.3285 0.4160 -0.4160 -0.2021 0.2021 0.4626 -0.4626 0.0360 -0.0360 0.7416 -0.7416
-0.5437 0.3411 -0.3411 -0.6812 0.6812 0.4461 -0.4461 -0.2694 0.2694 0.1357 -0.1357
0.3833 0.3342 -0.3342 0.3468 -0.3468 -0.2911 0.2911 0.6441 -0.6441 0.1286 -0.1286
-0.6184 -0.0442 0.0442 -0.4423 0.4423 0.6558 -0.6558 -0.6184 0.6184 0.5053 -0.5053
-0.2593 0.7726 -0.7726 -0.4232 0.4232 0.2686 -0.2686 0.3590 -0.3590 0.3997 -0.3997
Columns 199 through 209
0.7055 -0.7055 0.1173 -0.1173 0.6830 -0.6830 0.7609 -0.7609 0.1216 -0.1216 0.6523
0.0564 -0.0564 -0.7688 0.7688 0.2337 -0.2337 0.0814 -0.0814 0.3054 -0.3054 0.2422
-0.0638 0.0638 0.4484 -0.4484 0.1835 -0.1835 0.1562 -0.1562 0.4092 -0.4092 0.2423
0.6940 -0.6940 -0.2502 0.2502 0.3769 -0.3769 0.5018 -0.5018 -0.3840 0.3840 0.2842
0.1155 -0.1155 -0.3626 0.3626 0.5506 -0.5506 0.3718 -0.3718 0.7596 -0.7596 0.6134
Columns 210 through 220
-0.6523 0.6387 -0.6387 0.5260 -0.5260 0.7293 -0.7293 0.3707 -0.3707 0.6067 -0.6067
-0.2422 0.0387 -0.0387 0.1705 -0.1705 0.0729 -0.0729 0.0105 -0.0105 -0.5262 0.5262
-0.2423 0.4616 -0.4616 0.4366 -0.4366 0.3202 -0.3202 0.5838 -0.5838 0.1430 -0.1430
-0.2842 0.0691 -0.0691 -0.0274 0.0274 0.2977 -0.2977 -0.2992 0.2992 0.4794 -0.4794
-0.6134 0.6105 -0.6105 0.7091 -0.7091 0.5212 -0.5212 0.6574 -0.6574 -0.3238 0.3238
Columns 221 through 231
0.4099 -0.4099 0.1052 -0.1052 0.4120 -0.4120 0.4538 -0.4538 0.5272 -0.5272 0.1723
-0.7176 0.7176 -0.6822 0.6822 -0.0721 0.0721 -0.7208 0.7208 -0.1908 0.1908 -0.5185
0.5275 -0.5275 0.0208 -0.0208 0.6150 -0.6150 0.3369 -0.3369 0.6285 -0.6285 -0.1698
-0.0810 0.0810 0.1865 -0.1865 -0.2819 0.2819 0.1649 -0.1649 -0.1730 0.1730 0.4254
-0.1792 0.1792 -0.6987 0.6987 0.6062 -0.6062 -0.3659 0.3659 0.5107 -0.5107 -0.7012
Columns 232 through 242
-0.1723 0.4696 -0.4696 0.3864 -0.3864 0.5213 -0.5213 0.5055 -0.5055 -0.2686 0.2686
0.5185 -0.6920 0.6920 -0.0930 0.0930 -0.3748 0.3748 -0.1228 0.1228 -0.6150 0.6150
0.1698 0.2608 -0.2608 0.6271 -0.6271 0.6608 -0.6608 -0.6382 0.6382 -0.3959 0.3959
-0.4254 0.2566 -0.2566 -0.3146 0.3146 -0.1824 0.1824 -0.5669 0.5669 0.1872 -0.1872
0.7012 -0.4083 0.4083 0.5915 -0.5915 0.3433 -0.3433 0.0256 -0.0256 0.5982 -0.5982
A=ExA_11(6);
Calculate the Z-eigenpairs of the tensor A.
[lambda,V] = zeig(A)
lambda =
Columns 1 through 11
-133.2871 -133.2871 0 0 0 0 0 0 0 0 0
Columns 12 through 22
0 0 0 0 0 0 0 0 0 0 0
Columns 23 through 33
0 0 0 0 0 0 0 0 0 0 0
Columns 34 through 44
0 0 0 0 0 0 0 0 0 0 0
Columns 45 through 55
0 0 0 0 0 0 0 0 0 0 0
Columns 56 through 66
0 0 0 0 0 0 0 0 0 0 0
Columns 67 through 77
0 0 0 0 0 0 0 0 0 0 0
Columns 78 through 88
0 0 0 0 0 0 0 0 0 0 0
Columns 89 through 99
0 0 0 0 0 0 0 0 0 0 0
Columns 100 through 110
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Columns 397 through 407
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Columns 419 through 429
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Columns 441 through 451
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Columns 452 through 462
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Columns 463 through 473
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Columns 474 through 484
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Columns 485 through 495
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Columns 496 through 506
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Columns 507 through 517
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Columns 518 through 528
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Columns 529 through 539
0.0840 -0.0840 0.5030 -0.5030 0.0848 -0.0848 0.1637 -0.1637 0.5894 -0.5894 0.4161
0.0868 -0.0868 0.0193 -0.0193 0.1226 -0.1226 0.3463 -0.3463 0.0341 -0.0341 0.3914
-0.7774 0.7774 -0.1946 0.1946 -0.6211 0.6211 0.5444 -0.5444 0.3310 -0.3310 0.3570
0.0209 -0.0209 -0.7749 0.7749 -0.1815 0.1815 -0.1785 0.1785 -0.6362 0.6362 -0.6101
-0.0304 0.0304 0.2881 -0.2881 -0.1394 0.1394 -0.1719 0.1719 0.0486 -0.0486 -0.1765
0.6161 -0.6161 0.1591 -0.1591 0.7346 -0.7346 -0.7039 0.7039 -0.3670 0.3670 -0.3779
Columns 540 through 550
-0.4161 -0.4132 0.4132 0.2996 -0.2996 0.3308 -0.3308 0.2874 -0.2874 -0.2885 0.2885
-0.3914 0.4550 -0.4550 0.4819 -0.4819 0.2988 -0.2988 0.4886 -0.4886 0.1933 -0.1933
-0.3570 0.2890 -0.2890 0.4167 -0.4167 0.5186 -0.5186 -0.1553 0.1553 -0.4965 0.4965
0.6101 0.4570 -0.4570 -0.4010 0.4010 -0.4127 0.4127 -0.7868 0.7868 -0.2103 0.2103
0.1765 -0.2946 0.2946 -0.2848 0.2848 -0.1538 0.1538 0.1872 -0.1872 0.0357 -0.0357
0.3779 -0.4931 0.4931 -0.5124 0.5124 -0.5817 0.5817 -0.0210 0.0210 0.7664 -0.7664
Columns 551 through 561
0.6591 -0.6591 -0.0574 0.0574 0.3535 -0.3535 0.7101 -0.7101 0.2518 -0.2518 0.3050
-0.1162 0.1162 0.0940 -0.0940 0.5063 -0.5063 -0.1505 0.1505 0.3813 -0.3813 -0.3917
0.3275 -0.3275 0.7830 -0.7830 -0.0562 0.0562 -0.1728 0.1728 -0.7195 0.7195 0.6140
-0.6257 0.6257 -0.1165 0.1165 0.0460 -0.0460 -0.6294 0.6294 -0.2247 0.2247 -0.4116
-0.0141 0.0141 -0.1128 0.1128 -0.0695 0.0695 0.2153 -0.2153 -0.1400 0.1400 0.2588
-0.2306 0.2306 -0.5903 0.5903 -0.7801 0.7801 0.0274 -0.0274 0.4511 -0.4511 -0.3744
Columns 562 through 572
-0.3050 0.5773 -0.5773 0.7291 -0.7291 0.6400 -0.6400 -0.1774 0.1774 0.2537 -0.2537
0.3917 0.1344 -0.1344 -0.1147 0.1147 -0.0363 0.0363 0.1011 -0.1011 0.2184 -0.2184
-0.6140 0.3147 -0.3147 -0.0621 0.0621 -0.2661 0.2661 0.5090 -0.5090 0.6224 -0.6224
0.4116 -0.6623 0.6623 -0.6214 0.6214 -0.6693 0.6693 0.3271 -0.3271 -0.6245 0.6245
-0.2588 -0.0325 0.0325 0.2118 -0.2118 0.0786 -0.0786 0.0097 -0.0097 -0.2450 0.2450
0.3744 -0.3316 0.3316 -0.1426 0.1426 0.2531 -0.2531 -0.7695 0.7695 -0.2249 0.2249
Columns 573 through 583
0.5127 -0.5127 0.5314 -0.5314 0.0780 -0.0780 0.3703 -0.3703 0.4667 -0.4667 0.1056
-0.0355 0.0355 0.0122 -0.0122 -0.1325 0.1325 -0.4584 0.4584 0.1546 -0.1546 0.3476
0.4105 -0.4105 -0.1934 0.1934 -0.5656 0.5656 -0.0400 0.0400 -0.5308 0.5308 0.2428
-0.7375 0.7375 -0.7512 0.7512 -0.1836 0.1836 -0.5936 0.5936 -0.4942 0.4942 0.2142
0.0028 -0.0028 0.0674 -0.0674 0.0146 -0.0146 0.2223 -0.2223 -0.0728 0.0728 -0.0374
-0.1530 0.1530 0.3337 -0.3337 0.7890 -0.7890 0.4994 -0.4994 0.4765 -0.4765 -0.8728
Columns 584 through 594
-0.1056 0.3299 -0.3299 0.2887 -0.2887 0.3248 -0.3248 0.4539 -0.4539 0.3591 -0.3591
-0.3476 -0.1924 0.1924 -0.3591 0.3591 0.4996 -0.4996 0.5224 -0.5224 -0.3199 0.3199
-0.2428 0.6555 -0.6555 -0.1562 0.1562 -0.7233 0.7233 -0.1347 0.1347 -0.5260 0.5260
-0.2142 -0.5787 0.5787 -0.6202 0.6202 -0.1596 0.1596 -0.6109 0.6109 -0.3237 0.3237
0.0374 0.0754 -0.0754 0.3229 -0.3229 -0.1882 0.1882 -0.3424 0.3424 0.2339 -0.2339
0.8728 -0.2897 0.2897 0.5239 -0.5239 0.2468 -0.2468 0.1117 -0.1117 0.5766 -0.5766
Columns 595 through 605
-0.0810 0.0810 0.5596 -0.5596 0.2292 -0.2292 0.5066 -0.5066 0.4240 -0.4240 0.2102
0.0059 -0.0059 -0.2011 0.2011 0.4553 -0.4553 -0.0723 0.0723 -0.0725 0.0725 0.3204
0.5430 -0.5430 0.1240 -0.1240 0.4681 -0.4681 -0.4419 0.4419 0.5649 -0.5649 0.4322
0.2409 -0.2409 -0.7665 0.7665 -0.2869 0.2869 -0.5481 0.5481 -0.5546 0.5546 -0.0708
0.0870 -0.0870 0.1022 -0.1022 -0.2540 0.2540 0.0680 -0.0680 0.0669 -0.0669 -0.0831
-0.7956 0.7956 0.1818 -0.1818 -0.6117 0.6117 0.4876 -0.4876 -0.4287 0.4287 -0.8090
Columns 606 through 616
-0.2102 0.5633 -0.5633 0.6895 -0.6895 0.6626 -0.6626 0.4906 -0.4906 0.5211 -0.5211
-0.3204 0.3947 -0.3947 0.1187 -0.1187 0.2142 -0.2142 -0.0103 0.0103 -0.8183 0.8183
-0.4322 -0.1762 0.1762 0.1576 -0.1576 -0.0747 0.0747 0.2026 -0.2026 0.1824 -0.1824
0.0708 -0.6845 0.6845 -0.2370 0.2370 -0.7099 0.7099 -0.8138 0.8138 -0.0589 0.0589
0.0831 0.0578 -0.0578 -0.0780 0.0780 -0.0713 0.0713 0.2192 -0.2192 0.0279 -0.0279
0.8090 -0.1550 0.1550 -0.6507 0.6507 -0.0209 0.0209 -0.0883 0.0883 0.1458 -0.1458
Columns 617 through 627
-0.0119 0.0119 -0.0743 0.0743 0.6871 -0.6871 -0.1419 0.1419 0.4489 -0.4489 0.6143
-0.0553 0.0553 -0.3757 0.3757 -0.1183 0.1183 0.4264 -0.4264 0.1201 -0.1201 0.0427
0.8442 -0.8442 0.4923 -0.4923 0.2553 -0.2553 -0.7306 0.7306 -0.3895 0.3895 -0.2060
-0.2172 0.2172 0.2716 -0.2716 -0.4981 0.4981 0.4664 -0.4664 -0.5947 0.5947 -0.7123
-0.0794 0.0794 0.3369 -0.3369 0.1085 -0.1085 -0.1627 0.1627 -0.1026 0.1026 -0.0051
-0.4803 0.4803 -0.6509 0.6509 -0.4346 0.4346 0.1425 -0.1425 0.5178 -0.5178 0.2664
Columns 628 through 638
-0.6143 0.6396 -0.6396 0.0666 -0.0666 0.4161 -0.4161 0.2303 -0.2303 0.6770 -0.6770
-0.0427 0.1236 -0.1236 0.1891 -0.1891 0.4283 -0.4283 -0.0059 0.0059 0.1055 -0.1055
0.2060 -0.0985 0.0985 -0.7733 0.7733 0.3360 -0.3360 0.6131 -0.6131 -0.1777 0.1777
0.7123 -0.7406 0.7406 0.0262 -0.0262 -0.4292 0.4292 -0.1910 0.1910 -0.7003 0.7003
0.0051 -0.0475 0.0475 -0.1010 0.1010 -0.1967 0.1967 0.0802 -0.0802 0.0035 -0.0035
-0.2664 0.1233 -0.1233 0.5924 -0.5924 -0.5545 0.5545 -0.7267 0.7267 0.0921 -0.0921
Columns 639 through 649
0.3576 -0.3576 0.1462 -0.1462 0.8549 -0.8549 0.4069 -0.4069 0.2418 -0.2418 0.1374
-0.0766 0.0766 0.1764 -0.1764 0.0356 -0.0356 0.4041 -0.4041 -0.0019 0.0019 0.1028
-0.6544 0.6544 0.6365 -0.6365 -0.1239 0.1239 0.3207 -0.3207 -0.7722 0.7722 -0.6347
-0.2998 0.2998 -0.1753 0.1753 -0.2474 0.2474 -0.3275 0.3275 -0.1030 0.1030 -0.2105
0.0901 -0.0901 -0.0723 0.0723 -0.4278 0.4278 -0.1398 0.1398 0.0599 -0.0599 -0.1100
0.5831 -0.5831 -0.7116 0.7116 -0.0913 0.0913 -0.6644 0.6644 0.5754 -0.5754 0.7150
Columns 650 through 660
-0.1374 0.5603 -0.5603 -0.1494 0.1494 -0.1107 0.1107 0.1426 -0.1426 0.1171 -0.1171
-0.1028 0.1975 -0.1975 -0.0550 0.0550 -0.0574 0.0574 -0.2710 0.2710 0.4714 -0.4714
0.6347 0.0426 -0.0426 0.5716 -0.5716 0.6564 -0.6564 -0.3057 0.3057 0.5578 -0.5578
0.2105 -0.7789 0.7789 0.2785 -0.2785 0.1593 -0.1593 -0.4108 0.4108 -0.3220 0.3220
0.1100 -0.1492 0.1492 0.1026 -0.1026 0.0752 -0.0752 0.0437 -0.0437 -0.3431 0.3431
-0.7150 0.1276 -0.1276 -0.7482 0.7482 -0.7229 0.7229 0.8013 -0.8013 -0.4811 0.4811
Columns 661 through 671
0.2465 -0.2465 0.1472 -0.1472 0.5274 -0.5274 0.3738 -0.3738 0.1836 -0.1836 0.5052
-0.0662 0.0662 0.1240 -0.1240 0.1384 -0.1384 0.0659 -0.0659 0.1237 -0.1237 0.2727
0.7007 -0.7007 -0.4843 0.4843 0.3959 -0.3959 -0.4959 0.4959 0.6765 -0.6765 -0.3104
-0.3788 0.3788 -0.3598 0.3598 -0.6074 0.6074 -0.4847 0.4847 -0.2782 0.2782 -0.6431
0.0441 -0.0441 -0.1799 0.1799 -0.0351 0.0351 -0.0679 0.0679 -0.0639 0.0639 -0.1814
-0.5463 0.5463 0.7528 -0.7528 -0.4192 0.4192 0.6087 -0.6087 -0.6418 0.6418 0.3571
Columns 672 through 682
-0.5052 0.5263 -0.5263 0.5586 -0.5586 0.3346 -0.3346 0.4871 -0.4871 0.5905 -0.5905
-0.2727 0.1312 -0.1312 0.0520 -0.0520 -0.2086 0.2086 -0.1386 0.1386 0.0879 -0.0879
0.3104 -0.0318 0.0318 -0.6339 0.6339 0.6511 -0.6511 0.4926 -0.4926 0.0740 -0.0740
0.6431 -0.7785 0.7785 -0.4009 0.4009 -0.5381 0.5381 -0.5883 0.5883 -0.7892 0.7892
0.1814 -0.1322 0.1322 0.0838 -0.0838 0.1069 -0.1069 0.1215 -0.1215 -0.0671 0.0671
-0.3571 0.2850 -0.2850 0.3403 -0.3403 -0.3459 0.3459 -0.3743 0.3743 0.1039 -0.1039
Columns 683 through 693
0.4321 -0.4321 0.3642 -0.3642 0.2141 -0.2141 0.4856 -0.4856 0.5637 -0.5637 0.4629
-0.3675 0.3675 0.0467 -0.0467 0.2007 -0.2007 -0.2331 0.2331 0.4399 -0.4399 0.2078
0.4341 -0.4341 0.5142 -0.5142 -0.7393 0.7393 0.4491 -0.4491 0.1058 -0.1058 0.4496
-0.6736 0.6736 -0.2888 0.2888 -0.1517 0.1517 -0.6829 0.6829 -0.5534 0.5534 -0.5699
0.1892 -0.1892 0.0786 -0.0786 -0.1016 0.1016 0.1349 -0.1349 -0.1868 0.1868 -0.0962
-0.0143 0.0143 -0.7150 0.7150 0.5779 -0.5779 -0.1537 0.1537 -0.3693 0.3693 -0.4542
Columns 694 through 704
-0.4629 0.4390 -0.4390 0.4277 -0.4277 0.2798 -0.2798 0.5697 -0.5697 0.2336 -0.2336
-0.2078 0.1361 -0.1361 -0.3954 0.3954 -0.0264 0.0264 -0.0153 0.0153 -0.5346 0.5346
-0.4496 0.4979 -0.4979 0.2051 -0.2051 0.6259 -0.6259 0.0120 -0.0120 0.5911 -0.5911
0.5699 -0.6597 0.6597 -0.7078 0.7078 -0.2939 0.2939 -0.7865 0.7865 -0.3408 0.3408
0.0962 -0.1062 0.1062 0.1762 -0.1762 0.0758 -0.0758 -0.0170 0.0170 0.3359 -0.3359
0.4542 -0.3071 0.3071 0.2942 -0.2942 -0.6612 0.6612 0.2371 -0.2371 -0.2852 0.2852
Columns 705 through 715
-0.0004 0.0004 0.6086 -0.6086 0.4200 -0.4200 0.2862 -0.2862 0.5217 -0.5217 0.1885
-0.7485 0.7485 0.4025 -0.4025 0.1028 -0.1028 -0.2331 0.2331 0.4776 -0.4776 0.0910
0.4889 -0.4889 -0.1069 0.1069 -0.6979 0.6979 -0.2298 0.2298 -0.0078 0.0078 0.6650
-0.1114 0.1114 -0.6444 0.6444 -0.3117 0.3117 -0.5635 0.5635 -0.6445 0.6445 -0.2452
0.4300 -0.4300 -0.1900 0.1900 0.0085 -0.0085 0.0388 -0.0388 -0.2833 0.2833 -0.0260
-0.0587 0.0587 -0.0698 0.0698 0.4783 -0.4783 0.7014 -0.7014 -0.0636 0.0636 -0.6732
Columns 716 through 726
-0.1885 0.3873 -0.3873 0.5874 -0.5874 0.5304 -0.5304 -0.0953 0.0953 0.5840 -0.5840
-0.0910 -0.2294 0.2294 0.2000 -0.2000 0.1530 -0.1530 -0.0435 0.0435 0.3454 -0.3454
-0.6650 0.5955 -0.5955 0.2411 -0.2411 -0.1756 0.1756 0.8060 -0.8060 -0.1784 0.1784
0.2452 -0.5597 0.5597 -0.7017 0.7017 -0.7274 0.7274 -0.0662 0.0662 -0.6773 0.6773
0.0260 0.1385 -0.1385 -0.0889 0.0889 -0.1260 0.1260 -0.0227 0.0227 -0.1892 0.1892
0.6732 -0.3321 0.3321 -0.2379 0.2379 0.3456 -0.3456 -0.5783 0.5783 0.1156 -0.1156
Columns 727 through 728
0.6281 -0.6281
0.0717 -0.0717
0.3754 -0.3754
0.5687 -0.5687
-0.1060 0.1060
0.3533 -0.3533
A=ExA_12(4);
Calculate the Z-eigenpairs of the tensor A.
[lambda,V] = zeig(A)
lambda =
Columns 1 through 11
-132.3070 -0.7074 0 0 0 0 0 0 0 0 0
Columns 12 through 22
0 0 0 0 0 0 0 0 0 0 0
Columns 23 through 33
0 0 0 0 0 0 0 0 0 0 0
Columns 34 through 44
0 0 0 0 0 0 0 0 0 0 0
Columns 45 through 55
0 0 0 0 0 0 0 0 0 0 0
Columns 56 through 66
0 0 0 0 0 0 0 0 0 0 0
Columns 67 through 77
0 0 0 0 0 0 0 0 0 0 0
Columns 78 through 88
0 0 0 0 0 0 0 0 0 0 0
Columns 89 through 99
0 0 0 0 0 0 0 0 0 0 0
Columns 100 through 110
0 0 0 0 0 0 0 0 0 0 0
Columns 111 through 121
0 0 0 0 0 0 0 0 0 0 0
Columns 122 through 132
0 0 0 0 0 0 0 0 0 0 0
Columns 133 through 143
0 0 0 0 0 0 0 0 0 0 0
Columns 144 through 154
0 0 0 0 0 0 0 0 0 0 0
Columns 155 through 165
0 0 0 0 0 0 0 0 0 0 0
Columns 166 through 170
0 0 0 0.7074 132.3070
V =
Columns 1 through 11
-0.4030 0.9054 -0.4304 0.4304 -0.8246 0.8246 -0.6830 0.6830 -0.4088 0.4088 -0.7598
-0.4844 0.3082 0.8139 -0.8139 0.3077 -0.3077 -0.0573 0.0573 0.8126 -0.8126 0.0534
-0.5319 -0.0411 0.0069 -0.0069 0.0444 -0.0444 0.0123 -0.0123 0.0115 -0.0115 0.0612
-0.5657 -0.2890 -0.3903 0.3903 0.4726 -0.4726 0.7280 -0.7280 -0.4153 0.4153 0.6451
Columns 12 through 22
0.7598 -0.8494 0.8494 -0.8160 0.8160 -0.4029 0.4029 -0.7659 0.7659 -0.7478 0.7478
-0.0534 0.4315 -0.4315 0.1285 -0.1285 0.8398 -0.8398 -0.0034 0.0034 -0.0401 0.0401
-0.0612 0.1587 -0.1587 0.1422 -0.1422 -0.0828 0.0828 0.6271 -0.6271 0.6478 -0.6478
-0.6451 0.2592 -0.2592 0.5453 -0.5453 -0.3543 0.3543 0.1422 -0.1422 0.1401 -0.1401
Columns 23 through 33
-0.7313 0.7313 -0.7271 0.7271 -0.7090 0.7090 -0.6932 0.6932 -0.6322 0.6322 -0.4931
-0.0820 0.0820 0.1132 -0.1132 -0.1549 0.1549 0.6264 -0.6264 0.1692 -0.1692 -0.1540
0.6594 -0.6594 0.6744 -0.6744 0.6557 -0.6557 0.2833 -0.2833 0.7134 -0.7134 0.8353
0.1539 -0.1539 -0.0605 0.0605 0.2082 -0.2082 -0.2164 0.2164 -0.2505 0.2505 -0.1882
Columns 34 through 44
0.4931 -0.3445 0.3445 -0.2785 0.2785 0.2583 -0.2583 -0.3741 0.3741 -0.3314 0.3314
0.1540 -0.6308 0.6308 -0.0344 0.0344 -0.5546 0.5546 0.3783 -0.3783 -0.3913 0.3913
-0.8353 0.4257 -0.4257 0.8169 -0.8169 0.6875 -0.6875 0.5965 -0.5965 0.8492 -0.8492
0.1882 0.5496 -0.5496 -0.5039 0.5039 -0.3912 0.3912 -0.6009 0.6009 -0.1265 0.1265
Columns 45 through 55
-0.2670 0.2670 -0.2643 0.2643 -0.5537 0.5537 -0.2794 0.2794 -0.3598 0.3598 -0.0645
0.2663 -0.2663 -0.3865 0.3865 -0.0276 0.0276 0.2937 -0.2937 -0.3525 0.3525 -0.2075
0.6553 -0.6553 0.8588 -0.8588 0.8024 -0.8024 0.6393 -0.6393 0.8525 -0.8525 0.8128
-0.6545 0.6545 -0.2080 0.2080 -0.2211 0.2211 -0.6534 0.6534 -0.1402 0.1402 -0.5404
Columns 56 through 66
0.0645 -0.1404 0.1404 0.1244 -0.1244 -0.1380 0.1380 0.1276 -0.1276 -0.2140 0.2140
0.2075 -0.0459 0.0459 -0.5555 0.5555 -0.0117 0.0117 -0.5685 0.5685 0.1117 -0.1117
-0.8128 0.7862 -0.7862 0.7555 -0.7555 0.7711 -0.7711 0.7511 -0.7511 0.7354 -0.7354
0.5404 -0.6000 0.6000 -0.3243 0.3243 -0.6214 0.6214 -0.3103 0.3103 -0.6332 0.6332
Columns 67 through 77
-0.1685 0.1685 0.2422 -0.2422 -0.1979 0.1979 -0.1213 0.1213 -0.0975 0.0975 -0.1778
-0.0235 0.0235 -0.4938 0.4938 0.0784 -0.0784 -0.0879 0.0879 0.1148 -0.1148 0.0400
0.7861 -0.7861 0.7028 -0.7028 0.7480 -0.7480 0.7958 -0.7958 0.6903 -0.6903 0.7608
-0.5942 0.5942 -0.4512 0.4512 -0.6286 0.6286 -0.5867 0.5867 -0.7076 0.7076 -0.6229
Columns 78 through 88
0.1778 -0.1920 0.1920 -0.0376 0.0376 -0.1732 0.1732 -0.1999 0.1999 0.1076 -0.1076
-0.0400 0.0729 -0.0729 -0.2628 0.2628 0.0287 -0.0287 0.0922 -0.0922 -0.5336 0.5336
-0.7608 0.7490 -0.7490 0.8152 -0.8152 0.7646 -0.7646 0.7415 -0.7415 0.7666 -0.7666
0.6229 -0.6300 0.6300 -0.5147 0.5147 -0.6202 0.6202 -0.6338 0.6338 -0.3406 0.3406
Columns 89 through 99
-0.1586 0.1586 -0.2099 0.2099 -0.1685 0.1685 -0.1693 0.1693 -0.1309 0.1309 -0.0433
-0.0018 0.0018 0.1162 -0.1162 0.0176 -0.0176 0.0128 -0.0128 -0.0670 0.0670 -0.2492
0.7737 -0.7737 0.7316 -0.7316 0.7682 -0.7682 0.7707 -0.7707 0.7913 -0.7913 0.8146
-0.6133 0.6133 -0.6381 0.6381 -0.6174 0.6174 -0.6141 0.6141 -0.5936 0.5936 -0.5220
Columns 100 through 110
0.0433 -0.0579 0.0579 0.0818 -0.0818 -0.0564 0.0564 -0.1665 0.1665 -0.1523 0.1523
0.2492 -0.2384 0.2384 -0.8290 0.8290 -0.2249 0.2249 0.0480 -0.0480 -0.0184 0.0184
-0.8146 0.8175 -0.8175 0.4894 -0.4894 0.8140 -0.8140 0.7531 -0.7531 0.7789 -0.7789
0.5220 -0.5211 0.5211 0.2579 -0.2579 -0.5326 0.5326 -0.6346 0.6346 -0.6081 0.6081
Columns 111 through 121
-0.1751 0.1751 -0.1451 0.1451 -0.1226 0.1226 -0.1307 0.1307 -0.0884 0.0884 -0.1138
0.0309 -0.0309 -0.1147 0.1147 -0.0855 0.0855 -0.0915 0.0915 -0.1104 0.1104 -0.1042
0.7642 -0.7642 0.8126 -0.8126 0.7954 -0.7954 0.8003 -0.8003 0.7923 -0.7923 0.7990
-0.6199 0.6199 -0.5527 0.5527 -0.5873 0.5873 -0.5780 0.5780 -0.5935 0.5935 -0.5811
Columns 122 through 132
0.1138 -0.3469 0.3469 0.0553 -0.0553 -0.1225 0.1225 -0.0538 0.0538 -0.0224 0.0224
0.1042 0.5492 -0.5492 -0.4405 0.4405 -0.0816 0.0816 -0.2303 0.2303 -0.2904 0.2904
-0.7990 0.4269 -0.4269 0.7963 -0.7963 0.7940 -0.7940 0.8143 -0.8143 0.8145 -0.8145
0.5811 -0.6291 0.6291 -0.4108 0.4108 -0.5898 0.5898 -0.5301 0.5301 -0.5017 0.5017
Columns 133 through 143
0.0133 -0.0133 0.3347 -0.3347 -0.0716 0.0716 0.1469 -0.1469 -0.1670 0.1670 0.0314
-0.3374 0.3374 -0.8437 0.8437 -0.1857 0.1857 -0.6164 0.6164 0.0152 -0.0152 -0.3966
0.8076 -0.8076 0.4071 -0.4071 0.8095 -0.8095 0.7289 -0.7289 0.7689 -0.7689 0.8052
-0.4835 0.4835 0.1018 -0.1018 -0.5523 0.5523 -0.2594 0.2594 -0.6170 0.6170 -0.4398
Columns 144 through 154
-0.0314 0.3825 -0.3825 -0.5483 0.5483 0.2392 -0.2392 0.2103 -0.2103 0.1729 -0.1729
0.3966 -0.8600 0.8600 0.3666 -0.3666 -0.7363 0.7363 -0.6956 0.6956 0.0788 -0.0788
-0.8052 0.2291 -0.2291 0.6145 -0.6145 0.6208 -0.6208 0.6635 -0.6635 0.5569 -0.5569
0.4398 0.2483 -0.2483 -0.4329 0.4329 -0.1238 0.1238 -0.1782 0.1782 -0.8085 0.8085
Columns 155 through 165
0.2459 -0.2459 0.1150 -0.1150 0.2085 -0.2085 -0.0578 0.0578 0.0681 -0.0681 0.1463
-0.7450 0.7450 -0.5484 0.5484 -0.6950 0.6950 -0.2224 0.2224 -0.4598 0.4598 -0.8127
0.6101 -0.6101 0.7608 -0.7608 0.6646 -0.6646 0.8138 -0.8138 0.7906 -0.7906 0.5525
-0.1109 0.1109 -0.3274 0.3274 -0.1783 0.1783 -0.5337 0.5337 -0.3986 0.3986 0.1139
Columns 166 through 170
-0.1463 0.3066 -0.3066 -0.9054 0.4030
0.8127 -0.8154 0.8154 -0.3082 0.4844
-0.5525 0.4907 -0.4907 0.0411 0.5319
-0.1139 0.0181 -0.0181 0.2890 0.5657
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