Definition:Semi-Inner Product Space/Complex Field

Definition
Let $\Bbb F$ be a subfield of $\C$.

Let $V$ be a vector space over $\Bbb F$.

Let $\innerprod \cdot \cdot : V \times V \to \Bbb F$ 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) 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 Inner Product


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