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In [[mathematics]], a '''definite quadratic form''' is a [[quadratic form]] over some [[Real number|real]] [[vector space]] {{math|''V''}} that has the same [[positive and negative numbers|sign]] (always positive or always negative) for every nonzero vector [[Officer (armed forces)|of]] {{math|''V''}}. 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
==Associated symmetric bilinear form==
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