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 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.

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