Show that if $\displaystyle V = \mathbb C^n $

, then for any inner product on V , there

is a unique complex n × n matrix A such that $\displaystyle \langle \vec{v},\vec{w}\rangle =\vec{v}^T A \overline{\vec{w}} $ for

all $\displaystyle \ \vec{v},\vec{w}\in V$.

How to show existence?