Definition:Inner Product Norm

Definition
Let $\Bbb F$ be a subfield of $\C$.

Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\Bbb F$.

Then the inner product norm on $V$ is the mapping $\norm {\, \cdot \,} : V \to \R_{\ge 0}$ given by:


 * $\norm x = \sqrt {\innerprod x x}$

for each $x \in V$.

Also see

 * Inner Product Norm is Norm


 * Definition:Hilbert Space
 * Definition:Banach Space