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.