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Adding local short description: "Type of homogeneous polynomial of degree 2", overriding Wikidata description "quadratic form that is either greater then 0 except for 0 or less then 0 except for 0" (Shortdesc helper) |
→top: misuse of "even" |
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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 non-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
An '''indefinite''' quadratic form takes on both positive and negative values and is called an [[isotropic quadratic form]].
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