Definition:Semi-Inner Product Space/Complex Field

Definition
Let $\C$ be the field of real numbers.

Let $\GF$ be a subfield of $\C$.

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

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.

That is, a (complex) semi-inner product space is a vector space over a subfield of the complex numbers together with an associated complex semi-inner product.

Also see

 * User:Leigh.Samphier/Refactor/Definition:Complex Semi-Inner Product


 * User:Leigh.Samphier/Refactor/Definition:Real Semi-Inner Product Space


 * User:Leigh.Samphier/Refactor/Definition:Complex Inner Product Space