Definition:Inner Product Norm

Definition
Let $V$ be an inner product space over a subfield $\Bbb F$ of $\C$.

Let $\left \langle{\cdot, \cdot}\right \rangle$ be the inner product of $V$.

Then the inner product norm on $V$ is the map $\left\Vert{\cdot}\right\Vert: V \to \R_{\ge 0}$ given by
 * $\left\Vert{x}\right\Vert := \left\langle{x,x}\right\rangle^{1/2}$.

That the inner product norm is in fact a norm is proved in Inner Product Norm is Norm.