Definition:Semi-Inner Product Space

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Definition

A semi-inner product space is a vector space together with an associated semi-inner product.

Complex Semi-Inner Product Space

Let $V$ be a vector space over a complex subfield $\GF$.

Let $\innerprod \cdot \cdot : V \times V \to \GF$ be an complex semi-inner product on $V$.


We say that $\struct {V, \innerprod \cdot \cdot}$ is a (complex) semi-inner product space.

Real Semi-Inner Product Space

Let $V$ be a vector space over a real subfield $\GF$.

Let $\innerprod \cdot \cdot : V \times V \to \GF$ be an real semi-inner product on $V$.


We say that $\struct {V, \innerprod \cdot \cdot}$ is a (real) semi-inner product space.


Also see

  • Results about semi-inner product spaces can be found here.