MathGloss

Let $(V,F)$ be a vector space. A function $\langle\cdot,\cdot\rangle: V\times V \to F$ is an inner product on $V$ if

1. it is bilinear;
2. it is commutative;
3. $\langle v, v\rangle \geq 0$ for all $v \in V$ and $\langle v,v\rangle = 0$ if and only if $v=0$.

Wikidata ID: Q23924662

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