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searching for Definite quadratic form 13 found (40 total)

Perfect lattice (478 words) [view diff] exact match in snippet view article find links to article

its minimal vectors in the sense that there is only one positive definite quadratic form taking value 1 at all points of S. Perfect lattices were introduced

Binary quadratic form (4,936 words) [view diff] exact match in snippet view article find links to article

^{2}}q^{m^{2}+n^{2}}} , if f ( x , y ) {\displaystyle f(x,y)} is a positive definite quadratic form then ∑ ( m , n ) ∈ Z 2 q f ( m , n ) {\displaystyle \sum _{(m,n)\in

15 (number) (1,053 words) [view diff] exact match in snippet view article

being enclosed by the quadruplet (11, 13, 17, 19). If a positive definite quadratic form with integer matrix represents all positive integers up to 15,

Algebraic surface (973 words) [view diff] exact match in snippet view article find links to article

intersection form to { H } ⊥ {\displaystyle \{H\}^{\perp }} is a negative definite quadratic form. This theorem is proven using the Nakai criterion and the Riemann-Roch

Rotor (mathematics) (839 words) [view diff] exact match in snippet view article

group below. Let V be a vector space equipped with a positive definite quadratic form q, and let Cl(V) be the geometric algebra associated to V. The

Dvoretzky's theorem (1,058 words) [view diff] exact match in snippet view article find links to article

ε), there exists a subspace E ⊂ X of dimension k and a positive definite quadratic form Q on E such that the corresponding Euclidean norm | ⋅ | = Q ( ⋅

Néron–Tate height (1,802 words) [view diff] exact match in snippet view article find links to article

generally, h ^ L {\displaystyle {\hat {h}}_{L}} induces a positive definite quadratic form on the real vector space A ( K ) ⊗ R {\displaystyle A(K)\otimes

Divergence (statistics) (2,629 words) [view diff] exact match in snippet view article

M} , D ( p , p + d p ) {\displaystyle D(p,p+dp)} is a positive-definite quadratic form for infinitesimal displacements d p {\displaystyle dp} from p {\displaystyle

Gaussian function (5,019 words) [view diff] exact match in snippet view article find links to article

to which e is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will always be ellipses

Aleksei Pogorelov (2,777 words) [view diff] exact match in snippet view article find links to article

when the intrinsic geometry was given not by a smooth positive definite quadratic form, but simply by a metric space of a fairly general form. A breakthrough

Legendre transformation (8,906 words) [view diff] exact match in snippet view article find links to article

{\textstyle E_{x}} is strictly convex and bounded below by a positive definite quadratic form minus a constant, then the Legendre transform F L : E → E ∗ {\textstyle

Geometric algebra (13,797 words) [view diff] exact match in snippet view article find links to article

of two vectors in 3 {\displaystyle 3} dimensions with positive-definite quadratic form is closely related to their exterior product. Most instances of

Ising model (20,184 words) [view diff] exact match in snippet view article find links to article

{\displaystyle Z_{ij}\,\partial _{i}H\,\partial _{j}H} is a positive definite quadratic form, and can be used to define the metric for space. So any translationally