Does this even make sense what I translated into english?


PS. I am probably gonna delete this question eventually



Is it that only with normal matrices, the transition matrix to its [del: inherent] [ins: own] basis is unitary?
I am not sure I understand the question, but if you are talking about linear algebra over the complex numbers, then it is true that normal matrices (those which commute with their hermitian adjoint) are precisely those which can be diagonalised by a unitary transformation.
(This is proven in Herstein's *Topics in algebra*: §10 of the 1964 edition.)


