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 mapping $\left\Vert{\cdot}\right\Vert: V \to \R_{\ge 0}$ given by

$\left\Vert{x}\right\Vert := \left\langle{x,x}\right\rangle^{1/2}$.