MATLAB: Matlab cannot return orthogonal eigenvectors for a normal matrix

linear algebramatrix analysis

Now I have a normal matrix
A = [0 1 0 1 0 0 0 0 0;
     0 0 1 0 1 0 0 0 0;
     1 0 0 0 0 1 0 0 0;
     0 0 0 0 1 0 1 0 0;
     0 0 0 0 0 1 0 1 0;
     0 0 0 1 0 0 0 0 1;
     1 0 0 0 0 0 0 1 0;
     0 1 0 0 0 0 0 0 1;
     0 0 1 0 0 0 1 0 0];
It should have orthogonal eigenvectors, however, matlab eig function cannot return the orthogonal ones. Is it the problem with the algorithm?

Best Answer

Hello Ran, If a matrix A is normal it can be diagonalized with a unitary matrix, A = U D U', but no one is saying that the set of eigenvectors of A necessarily provides the matrix U. Lot of times it doesn't.
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