Definition 12.17

A vector space $E$ is called an *inner product space* if the real number $\langle p\text{,}q\rangle $, called the *inner product* of $p$ and $q$, is assigned to each $p\text{,}q\in E$ such that the following axioms hold:

(a) (*Nonnegativity*) $\forall p\in E\text{,}\langle p\text{,}p\rangle \ge 0$.

(b) (*Nondegeneracy*) ...