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 eigenvalues and eigenvectors.
[lambda,V] = teig(A,'symmetric')
lambda =
Columns 1 through 5
-2.6841 + 0.0000i -1.8370 - 1.1859i -1.8370 + 1.1859i -1.6969 - 0.2787i -1.6969 + 0.2787i
Columns 6 through 10
-1.6687 - 3.4926i -1.6687 + 3.4926i -1.0358 - 0.9961i -1.0358 + 0.9961i -0.6665 - 0.0000i
Columns 11 through 15
-0.0887 + 0.0000i 0.2499 - 0.0000i 0.2528 + 0.0000i 0.4108 - 0.0000i 0.7228 - 0.0000i
Columns 16 through 20
0.7281 - 0.3884i 0.7281 + 0.3884i 0.7732 - 0.8385i 0.7732 + 0.8385i 0.8944 - 0.0000i
Columns 21 through 25
0.9780 - 0.0000i 1.2553 - 1.0002i 1.2553 + 1.0002i 1.8063 + 0.7308i 1.8063 - 0.7308i
Columns 26 through 27
1.9316 + 0.0000i 2.3129 - 0.0000i
V =
Columns 1 through 5
-0.8983 - 0.0000i 0.0150 + 0.9127i 0.0150 - 0.9127i 0.0141 - 0.8848i 0.0141 + 0.8848i
1.0000 + 0.0000i -0.4541 + 0.0486i -0.4541 - 0.0486i 0.2039 - 0.7897i 0.2039 + 0.7897i
0.5814 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i
Columns 6 through 10
0.0228 + 0.9552i 0.0228 - 0.9552i 0.2959 - 0.1603i 0.2959 + 0.1603i 0.2296 + 0.0000i
-0.0397 - 0.9609i -0.0397 + 0.9609i 0.0757 - 0.8626i 0.0757 + 0.8626i -0.2584 + 0.0000i
1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i
Columns 11 through 15
1.0000 + 0.0000i 0.4213 - 0.0000i 1.0000 + 0.0000i -0.2073 + 0.0000i 1.0000 + 0.0000i
0.8054 + 0.0000i 1.0000 + 0.0000i 0.1020 + 0.0000i 0.5241 + 0.0000i 0.5792 - 0.0000i
0.1703 + 0.0000i 0.2203 - 0.0000i -0.0868 - 0.0000i 1.0000 - 0.0000i 0.9396 + 0.0000i
Columns 16 through 20
0.1469 - 0.5485i 0.1469 + 0.5485i 1.0000 - 0.0000i 1.0000 + 0.0000i 0.6193 + 0.0000i
1.0000 + 0.0000i 1.0000 + 0.0000i 0.1514 + 0.8045i 0.1514 - 0.8045i 0.9542 + 0.0000i
-0.2765 + 0.1510i -0.2765 - 0.1510i 0.3994 - 0.0446i 0.3994 + 0.0446i 1.0000 + 0.0000i
Columns 21 through 25
-0.1546 - 0.0000i 0.2248 - 0.9012i 0.2248 + 0.9012i 1.0000 + 0.0000i 1.0000 + 0.0000i
1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 - 0.0000i 0.1192 + 0.6584i 0.1192 - 0.6584i
-0.6742 + 0.0000i 0.6678 + 0.0395i 0.6678 - 0.0395i -0.9237 + 0.0724i -0.9237 - 0.0724i
Columns 26 through 27
1.0000 + 0.0000i -0.9677 + 0.0000i
-0.7471 + 0.0000i -0.7966 - 0.0000i
0.7928 - 0.0000i 1.0000 + 0.0000i