Definition:Inner Product Norm
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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
- $\left\Vert{x}\right\Vert := \left\langle{x,x}\right\rangle^{1/2}$.
Also see
Sources
- 1990: John B. Conway: A Course in Functional Analysis $\S I.1$