My TA said that every hermitian matix implies transformation is hermitian because you can find orthonormal basis for every hermitian matrix and therefore transformation is hermitian.
Is that true??
What about the converse?
If the transformation is hermitian, then matrix of T is hermitian?
Yes, if you take the matrix with respect to an orthonormal basis. If $\{e_1,\ldots,e_n\}$ is an orthonormal basis, then $$ T_{kj}=\langle Te_j,e_k\rangle=\langle e_j,T^*e_k\rangle=\langle e_j,Te_k\rangle=\overline{\langle Te_k,e_j\rangle}=\overline{T_{jk}}. $$