Axiom:Real 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 inner product $\innerprod \cdot \cdot$ satisfies the following axioms:

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

Also see

 * Definition:Real Inner Product


 * Axiom:Complex Inner Product Axioms


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