Is a unitary matrix hermitian? If this is true then you should go to the first result which is product of two hermitian matrices is hermitian.
In the following document, p. 91 (or p. 4 of the PDF) , heading 6.03, it is stated that "The transform of a hermitian matrix by a unitary matrix is hermitian." Apparently the proof is obvious, but it's not that obvious to me... could someone clarify this? Thank you!