Suppose $D = P^{-1} A P$. When is $P$ unitary?
In other words, what kind of a matrix $A$ should be, such that $D=P^{\dagger}AP$? i.e. what are the conditions a matrix must have to be able to diagonalize it using unitary matrices?
2026-03-29 01:35:47.1774748147
What kind of a matrix has a unitary diagonalizing matrix?
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Any normal matrix ($AA^{\dagger}=A^{\dagger}A$) is unitarily diagonalisable.
In particular, any hermitian matrix is unitarily diagonalisable, since $H=H^{\dagger}$.