Axiom:Real Semi-Inner Product Axioms

Definition
Let $\R$ be the field of real numbers.

Let $\GF$ be a subfield of $\R$.

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 (real) semi-inner product axioms $\innerprod \cdot \cdot$ satisfies the following axioms:

Also see

 * User:Leigh.Samphier/Refactor/Axiom:Complex Semi-Inner Product Axioms, the semi-inner product axioms on a Definition:Complex Sub-Field


 * User:Leigh.Samphier/Refactor/Definition:Real Semi-Inner Product


 * User:Leigh.Samphier/Refactor/Definition:Real Semi-Inner Product Space


 * User:Leigh.Samphier/Refactor/Definition:Real Inner Product, a semi-inner product with the additional property of positiveness.