The transform of a Hermitian matrix by a unitary matrix is Hermitian In the following document,  p91 (or p4 of the PDF) , section 6.03, it is stated that "The transform of a hermitian matrix by a unitary matrix is hermitian." Apparently the proof is obvious, but not to me... could someone elaborate?

A matrix is hermitian if $ A^\ast = A$ where $A^\ast$ is the conjugated and transposed of $A$. 
Unitary matrices have the property that $U\cdot U^\ast= Id$ where Id is the identity. So in special we have $U^\ast =U^{-1}$. 
Now we look at the transformed hermitian: 
$$ U^{-1} A U=U^\ast A U$$ 
if conjugate and transpose this we have 
$$ (U^\ast A U)^\ast = U^\ast A^\ast (U^\ast)^\ast= U^\ast A^\ast U=U^\ast A U$$
which says that the transformed still hermitian.
