Axiom:Complex Inner Product Axioms

Definition
Let $\C$ be the field of complex 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 a mapping.

The mapping $\innerprod \cdot \cdot$ satisfies the (complex) inner product axioms $\innerprod \cdot \cdot$ satisfies the following axioms:

Also see

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


 * User:Leigh.Samphier/Refactor/Axiom:Real Inner Product Axioms


 * Definition:Semi-Inner Product, a slightly more general concept.