Definition:Semi-Inner Product/Real Field

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

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

Let $V$ be a vector space over $\GF$.

A semi-inner product is a mapping $\innerprod \cdot \cdot: V \times V \to \GF$ that satisfies the semi-inner product axioms:

Also see

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