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- Isotropic_quadratic_form abstract "In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise the quadratic form is anisotropic. More precisely, if q is a quadratic form on a vector space V over F, then a non-zero vector v in V is said to be isotropic if q(v) = 0. A quadratic form is isotropic if and only if there exists a non-zero isotropic vector for that quadratic form. Suppose that (V,q) is quadratic space and W is a subspace. Then W is called an isotropic subspace of V if some vector in it is isotropic, a totally isotropic subspace if all vectors in it are isotropic, and an anisotropic subspace if it does not contain any (non-zero) isotropic vectors. The isotropy index of a quadratic space is the maximum of the dimensions of the totally isotropic subspaces.A quadratic form q on a finite-dimensional real vector space V is anisotropic if and only if q is a definite form: either q is positive definite, i.e. q(v) > 0 for all non-zero v in V ; or q is negative definite, i.e. q(v) < 0 for all non-zero v in V. More generally, if the quadratic form is non-degenerate and has the signature (a,b), then its isotropy index is the minimum of a and b.".
- Isotropic_quadratic_form wikiPageExternalLink pete_clark.pdf.
- Isotropic_quadratic_form wikiPageID "10917170".
- Isotropic_quadratic_form wikiPageRevisionID "558350582".
- Isotropic_quadratic_form hasPhotoCollection Isotropic_quadratic_form.
- Isotropic_quadratic_form subject Category:Bilinear_forms.
- Isotropic_quadratic_form subject Category:Quadratic_forms.
- Isotropic_quadratic_form type Abstraction100002137.
- Isotropic_quadratic_form type BilinearForms.
- Isotropic_quadratic_form type Form106290637.
- Isotropic_quadratic_form type LanguageUnit106284225.
- Isotropic_quadratic_form type Part113809207.
- Isotropic_quadratic_form type QuadraticForms.
- Isotropic_quadratic_form type Relation100031921.
- Isotropic_quadratic_form type Word106286395.
- Isotropic_quadratic_form comment "In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise the quadratic form is anisotropic. More precisely, if q is a quadratic form on a vector space V over F, then a non-zero vector v in V is said to be isotropic if q(v) = 0. A quadratic form is isotropic if and only if there exists a non-zero isotropic vector for that quadratic form. Suppose that (V,q) is quadratic space and W is a subspace.".
- Isotropic_quadratic_form label "Isotropic quadratic form".
- Isotropic_quadratic_form label "迷向二次型".
- Isotropic_quadratic_form sameAs m.02qtz8t.
- Isotropic_quadratic_form sameAs Q4968811.
- Isotropic_quadratic_form sameAs Q4968811.
- Isotropic_quadratic_form sameAs Isotropic_quadratic_form.
- Isotropic_quadratic_form wasDerivedFrom Isotropic_quadratic_form?oldid=558350582.
- Isotropic_quadratic_form isPrimaryTopicOf Isotropic_quadratic_form.