= Solution
For a complex <matrix>, its <Hermitian conjugate> is obtained by transposing and taking entrywise <complex conjugates>:
$$
(A^\dagger)_{ij}=\overline{A_{ji}},\qquad A^\dagger=\overline A^{\,T}.
$$
The defining conditions are
$$
\boxed{A\text{ is Hermitian}\iff A^\dagger=A,\qquad A\text{ is unitary}\iff A^\dagger A=AA^\dagger=I.}
$$
For a square <matrix>, either one of the two inverse identities in the <unitary matrix> condition implies the other. A <Hermitian matrix> may have complex entries, but its diagonal entries are real.
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