Create two tensors, A and B,
then solve the generalized eigenvalue problem for the eigenvalues
and eigenvectors of the pair (A,B).
A(1,1,1) = 1; A(1,2,1) = 2; A(2,1,1) = 3; A(2,2,1) = 4;
A(1,1,2) = 5; A(1,2,2) = 6; A(2,1,2) = 7; A(2,2,2) = 0;
B = eye(2);
[lambda,V] = teneig(A,B)
lambda =
-9.8995 - 0.0000i -4.3820 - 0.0000i -0.4105 - 0.0000i 0.4105 + 0.0000i 4.3820 - 0.0000i 9.8995 + 0.0000i
V =
1.0000 + 0.0000i -0.5252 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i -0.5252 + 0.0000i 1.0000 + 0.0000i
1.0000 - 0.0000i 1.0000 + 0.0000i -0.2626 - 0.0000i -0.2626 - 0.0000i 1.0000 + 0.0000i 1.0000 - 0.0000i
Create two tensors, A and B,
then solve the generalized mode k-eigenvalue problem for the mode 3-eigenvalues
and mode 3-eigenvectors of the pair (A,B).
A(1,1,1) = 1; A(1,2,1) = 2; A(2,1,1) = 3; A(2,2,1) = 4;
A(1,1,2) = 5; A(1,2,2) = 6; A(2,1,2) = 7; A(2,2,2) = 0;
B = eye(2);
[lambda,V] = teneig(A,B,3)
lambda =
-9.4025 + 0.0000i -4.3007 + 0.0000i -0.2936 - 0.0000i 0.2936 + 0.0000i 4.3007 + 0.0000i 9.4025 - 0.0000i
V =
0.6950 - 0.0000i -0.4323 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 0.6950 - 0.0000i
1.0000 + 0.0000i 1.0000 + 0.0000i -0.3756 - 0.0000i -0.3756 - 0.0000i -2.3133 + 0.0000i 1.0000 + 0.0000i
Create a cell of string P which equals Av m.
P = {'3*x1^4+x2^4'};
Calculate the eigenvalues, lambda,
the eigenvectors, V, the residule, res and the reciprocal of the condition number, cnd.
[lambda, V, res, cnd] = teneig(P)
lambda =
1.0000 - 0.0000i 1.0000 - 0.0000i 1.0000 - 0.0000i 3.0000 - 0.0000i 3.0000 + 0.0000i 3.0000 + 0.0000i
V =
-0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i
1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i
res =
1.0e-15 *
0.0362 0.0997 0.1115 0.0007 0.6281 0.1140
cnd =
1.0e-10 *
0.2067 0.9141 0.2067 0.0145 0.1698 0.1655