When searching for matrices that are similar to a diagonal matrix but not in a unitary way then a first hint would be to exclude the normal ones. But apart from that is there a general form for such matrices as the Jordan decomposition for nondiagonalizable matrices?
2026-03-28 01:26:10.1774661170
Non-Unitarily Diagonalizable Matrices
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Any matrix is similar to its Jordan Canonical form. The matrices implementing the "similarity" need not be unitary.