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 real tensor A is nonsymmetric.
Convert it to a symmetric tensor and calculate the Z-Eigenvalues and Z-Eigenvectors.
[lambda,V] = zeig(A,'symmetric')
lambda =
Columns 1 through 13
-1.0954 -1.0954 -0.5629 -0.5629 -0.0451 -0.0451 0.1735 0.1735 0.2433 0.2433 0.2628 0.2628 0.2682
Columns 14 through 22
0.2682 0.3633 0.3633 0.5105 0.5105 0.8169 0.8169 0.8893 0.8893
V =
Columns 1 through 13
-0.5915 0.5915 -0.1762 0.1762 -0.7797 0.7797 -0.3357 0.3357 -0.9895 0.9895 -0.1318 0.1318 -0.6099
0.7467 -0.7467 0.1796 -0.1796 -0.6135 0.6135 -0.9073 0.9073 -0.0947 0.0947 0.4425 -0.4425 -0.4362
0.3043 -0.3043 -0.9678 0.9678 -0.1250 0.1250 -0.2531 0.2531 0.1088 -0.1088 0.8870 -0.8870 -0.6616
Columns 14 through 22
0.6099 -0.2676 0.2676 -0.3598 0.3598 -0.8412 0.8412 -0.6672 0.6672
0.4362 -0.6447 0.6447 0.7780 -0.7780 0.2635 -0.2635 -0.2471 0.2471
0.6616 -0.7160 0.7160 -0.5150 0.5150 -0.4722 0.4722 0.7027 -0.7027