A = zeros(3,3,3,3);
A(1,1,1,1) = 0.2883; A(1,1,1,2) = -0.0031; A(1,1,1,3) = 0.1973;
A(1,1,2,2) = -0.2485; A(1,1,2,3) = -0.2939; A(1,1,3,3) = 0.3847;
A(1,2,2,2) = 0.2972; A(1,2,2,3) = 0.1862; A(1,2,3,3) = 0.0919;
A(1,3,3,3) = -0.3619; A(2,2,2,2) = 0.1241; A(2,2,2,3) = -0.3420;
A(2,2,3,3) = 0.2127; A(2,3,3,3) = 0.2727; A(3,3,3,3) = -0.3054;
Note that the above tensor A is nonsymmetric.
Convert it to a symmetric tensor and calculate the E-eigenvalues and E-eigenvectors.
[lambda,V] = eeig(A,'symmetric')
lambda =
Columns 1 through 6
-1.0954 + 0.0000i -1.0954 - 0.0000i -0.5629 + 0.0000i -0.5629 + 0.0000i -0.0451 - 0.0000i -0.0451 + 0.0000i
Columns 7 through 12
0.1735 + 0.0000i 0.1735 + 0.0000i 0.2433 - 0.0000i 0.2433 + 0.0000i 0.2628 + 0.0000i 0.2628 - 0.0000i
Columns 13 through 18
0.2682 - 0.0000i 0.2682 - 0.0000i 0.3633 - 0.0000i 0.3633 + 0.0000i 0.5105 + 0.0000i 0.5105 - 0.0000i
Columns 19 through 24
0.6764 - 0.0014i 0.6764 + 0.0014i 0.6764 - 0.0014i 0.6764 + 0.0014i 0.8169 - 0.0000i 0.8169 + 0.0000i
Columns 25 through 26
0.8893 + 0.0000i 0.8893 - 0.0000i
V =
Columns 1 through 6
-0.5915 + 0.0000i 0.5915 + 0.0000i -0.1762 + 0.0000i 0.1762 + 0.0000i -0.7797 - 0.0000i 0.7797 - 0.0000i
0.7467 - 0.0000i -0.7467 + 0.0000i 0.1796 - 0.0000i -0.1796 - 0.0000i -0.6135 + 0.0000i 0.6135 + 0.0000i
0.3043 + 0.0000i -0.3043 + 0.0000i -0.9678 - 0.0000i 0.9678 - 0.0000i -0.1250 + 0.0000i 0.1250 - 0.0000i
Columns 7 through 12
-0.3357 + 0.0000i 0.3357 - 0.0000i -0.9895 + 0.0000i 0.9895 + 0.0000i -0.1318 + 0.0000i 0.1318 + 0.0000i
-0.9073 - 0.0000i 0.9073 + 0.0000i -0.0947 - 0.0000i 0.0947 - 0.0000i 0.4425 + 0.0000i -0.4425 + 0.0000i
-0.2531 + 0.0000i 0.2531 + 0.0000i 0.1088 + 0.0000i -0.1088 + 0.0000i 0.8870 - 0.0000i -0.8870 - 0.0000i
Columns 13 through 18
-0.6099 - 0.0000i 0.6099 - 0.0000i -0.2676 - 0.0000i 0.2676 + 0.0000i -0.3598 + 0.0000i 0.3598 + 0.0000i
-0.4362 - 0.0000i 0.4362 + 0.0000i -0.6447 + 0.0000i 0.6447 + 0.0000i 0.7780 - 0.0000i -0.7780 - 0.0000i
-0.6616 + 0.0000i 0.6616 - 0.0000i -0.7160 - 0.0000i 0.7160 + 0.0000i -0.5150 + 0.0000i 0.5150 - 0.0000i
Columns 19 through 24
-0.2945 + 0.0578i -0.2945 - 0.0578i 0.2945 - 0.0578i 0.2945 + 0.0578i -0.8412 + 0.0000i 0.8412 + 0.0000i
-0.8215 - 0.0358i -0.8215 + 0.0358i 0.8215 + 0.0358i 0.8215 - 0.0358i 0.2635 + 0.0000i -0.2635 + 0.0000i
0.4937 - 0.0252i 0.4937 + 0.0252i -0.4937 + 0.0252i -0.4937 - 0.0252i -0.4722 - 0.0000i 0.4722 - 0.0000i
Columns 25 through 26
-0.6672 + 0.0000i 0.6672 - 0.0000i
-0.2471 + 0.0000i 0.2471 + 0.0000i
0.7027 + 0.0000i -0.7027 + 0.0000i