Axiom:Complex Semi-Inner Product Axioms

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

Let $\innerprod \cdot \cdot: V \times V \to \GF$ be a mapping.

The mapping $\innerprod \cdot \cdot$ is a complex semi-inner product $\innerprod \cdot \cdot$ satisfies the following axioms:

These criteria are called the (complex) semi-inner product axioms.

Also see

 * Axiom:Real Semi-Inner Product Axioms, the semi-inner product axioms over a real subfield


 * Definition:Complex Semi-Inner Product


 * Definition:Complex Semi-Inner Product Space


 * Definition:Complex Inner Product, a semi-inner product with the additional property of positiveness.