Definite quadratic form

Definite quadratic form

In mathematics, a definite quadratic form is a real-valued quadratic form over some vector space V that has the same sign (always positive or always negative) for every nonzero vector of V. The definite quadratic forms correspond in one-to-one way to the (symmetric) definite bilinear forms over the same space.

A semidefinite (or semi-definite) quadratic form is defined in the same way, except that "positive" and "negative" are replaced by "not negative" and "not positive", respectively. The semidefinite quadratic forms correspond to the symmetric semidefinite bilinear forms.


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