# positive definite form

A bilinear form $B$ on a real or complex vector space $V$ is 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 $B(x,x)\geq 0$ for all vectors $x\in V$, then we say $B$ is nonnegative definite. Likewise, if $B(x,x)\leq 0$ 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.

 Title positive definite form Canonical name PositiveDefiniteForm Date of creation 2013-03-22 12:25:50 Last modified on 2013-03-22 12:25:50 Owner djao (24) Last modified by djao (24) Numerical id 5 Author djao (24) Entry type Definition Classification msc 11E39 Classification msc 15A63 Classification msc 47A07 Synonym positive definite Synonym negative definite form Synonym negative definite Synonym indefinite form Synonym indefinite Synonym nonnegative definite Synonym nonpositive definite