Suppose there is a transformation T and let A be a matrix representation of T with chosen basis. If I find out the eigenvalues of matrix A, these eigenvalues will be the eigenvalues of the transformation T?
Then what about eigenvectors of T? As far as I know, similar matrices have same eigenvalues, so any matrix representation of T with different basis has same eigenvalues, but eigenvectors corresponding to eigenvalues are dependent of matrix representation.
Then, what can I say about eigenvectors of T by just looking at the eigenvectors of matrices?
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