Definite quadratic form: Difference between revisions

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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 nonzeronon-zero vector 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 much the same way, except that "always positive" and "always negative" are replaced by "always nonnegative" and "always nonpositive", respectively. In other words, it may take on zero values even for non-zero vectors of {{math|''V''}}.

An '''indefinite''' quadratic form takes on both positive and negative values and is called an [[isotropic quadratic form]].