If $V$ is a finite $n$-dimensional complex vector space with a hermitian form $h$ then $h$ is given by a hermitian matrix $A$ with the transformation law $P^{t}A\bar{P}$ where $P$ is an invertible $n\times n$ matrix and $^\bar{}$ denotes complex conjugation.
If $V$ is unitary, in other words $h$ is positive definite, then why must $P$ be a unitary matrix?
Many thanks!