If $A$ is an $n \times n$ Hermitian matrix, and $S$ is an $n \times n$ matrix, then $S A S^*$ is also Hermitian.
Why is this true? I have seen this claim made in several places but can't find a proof.
2026-03-25 11:02:20.1774436540
If $A$ is a Hermitian matrix then $SAS^*$ is also Hermitian
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Hint: Calculate $(SAS^*)^*$ using rules like $(AB)^*=B^*A^*$