diagonalizing a matrix in two way

I diagonalize a matrix by using eig and then I change the matrix to symbolic for by A=sym(A) and them diagonalize it again, the two orthogonal matrix that I get from this two ways are not the same and I do not know why. ``

Answer 1

[Walter Oevel]

Eigenvectors are not unique.

1) The ordering as columns/rows of a matrix must match the ordering of the eigenvalues in the diagonalized matrix.

2) The normalization of the eigenvectors is rather arbitrary.

The strategies for ordering and normalization in MATLAB's eig may be different for numerical input and for symbolic input.

If you have more detailed questions, please provide more information on the example(s) that puzzle(s) you (in particular, provide the input matrix).

Regards,

Walter Oevel