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In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of 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 for some non-zero vectors of V.

Attributes	Values
rdfs:label	Definite quadratic form (en)
rdfs:comment	In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of 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 for some non-zero vectors of V. (en)
sameAs	Definite form Definite form
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Math dbt:Reflist dbt:Short_description dbt:Lang_Algebra
Subject	Quadratic forms Linear algebra
gold:hypernym	Form
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Definite_quadratic_form?oldid=1069030259&ns=0
Wikipage page ID	20437320 (xsd:integer)
page length (characters) of wiki page	7031 (xsd:nonNegativeInteger)
Wikipage revision ID	1069030259 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic forms Linear algebra Positive-definite function Quadratic form Second partial derivative test Definite matrix Hyperbola Conic section Eigenvalues and eigenvectors Minor (linear algebra) Ordered field Ellipse Ergebnisse der Mathematik und ihrer Grenzgebiete Symmetric bilinear form Symmetric matrix Derivative test Diagonal matrix Invertible matrix Parabola Transpose Vector space Euclidean space Euclidean vector Isotropic quadratic form Mathematical optimization Mathematics Matrix (mathematics) Matrix calculus Negative number Polarization identity Real number Regression analysis
has abstract	In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of 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 for some non-zero vectors of V. An indefinite quadratic form takes on both positive and negative values and is called an isotropic quadratic form. More generally, these definitions apply to any vector space over an ordered field. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Definite_quadratic_form
is Wikipage redirect of	Semi-definite Semi-definite bilinear form Semi-definite form Semi-definite quadratic form Semidefinite Semidefinite bilinear form Semidefinite form Semidefinite quadratic form Positive-definite bilinear form Positive-definite form Positive-definite quadratic form Positive Definite Quadratic Form Positive definite bilinear form Positive definite form Positive definite quadratic form Positive semi-definite bilinear form Positive semi-definite form Positive semi-definite quadratic form Positive semidefinite bilinear form Positive semidefinite form Positive semidefinite quadratic form Definite bilinear form Indefinite form Indefinite quadratic form Negative-definite bilinear form Negative-definite form Negative-definite quadratic form Negative definite bilinear form Negative definite form Negative definite quadratic form Negative semi-definite Negative semi-definite bilinear form Negative semi-definite form Negative semi-definite quadratic form Negative semidefinite Negative semidefinite bilinear form Negative semidefinite form Negative semidefinite quadratic form
is Link from a Wikipage to another Wikipage of	Norm (mathematics) Null vector 15 and 290 theorems Abelian variety Absolute value Affine space Algebraic structure BRST quantization Okubo algebra Cartan decomposition Cartan–Dieudonné theorem Cartan–Karlhede algorithm

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