positive definite form

A bilinear formPlanetmathPlanetmath B on a real or complex vector space V is positive definitePlanetmathPlanetmath if B(x,x)>0 for all nonzero vectors xV. On the other hand, if B(x,x)<0 for all nonzero vectors xV, then we say B is negative definite. If B(x,x)0 for all vectors xV, then we say B is nonnegative definite. Likewise, if B(x,x)0 for all vectors xV, 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