positive definite form

A bilinear form $B$ on a real or complex vector space $V$ is positive definite if $B(x,x) > 0$ for all nonzero vectors $x \in V$ . On the other hand, if $B(x,x) < 0$ for all nonzero vectors $x \in V$ , then we say $B$ is negative definite. If $B(x,x) \ge 0$ for all vectors $x \in V$ , then we say $B$ is nonnegative definite. Likewise, if $B(x,x) \le 0$ for all vectors $x \in V$ , then we say $B$ is nonpositive definite.

A form which is neither positive definite nor negative definite is called indefinite.