Definition:Inner Product Space/Complex Field
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Definition
Let $V$ be a vector space over a complex subfield $\GF$.
Let $\innerprod \cdot \cdot : V \times V \to \GF$ be an complex inner product on $V$.
We say that $\struct {V, \innerprod \cdot \cdot}$ is a (complex) inner product space.
That is, a (complex) inner product space is a complex vector space together with an associated complex inner product.
Also see
- Results about inner product spaces can be found here.