Axiom:Real Semi-Inner Product Axioms

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

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

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

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

Also see

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


 * Definition:Real Semi-Inner Product


 * Definition:Real Semi-Inner Product Space


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