What is "definite quadratic form"

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every nonzero vector of . According to that sign, the quadratic form is called positive definite or negative definite.

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. An indefinite quadratic form is one that takes on both positive and negative values.

More generally, the definition applies to a vector space over an ordered field.