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)...
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quadratic form over K. If K = R, and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form;...
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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 it is a definite quadratic...
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In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x...
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Positive-definite kernel Positive-definite matrix Positive-definite quadratic form Fasshauer, Gregory E. (2011), "Positive definite kernels: Past, present and...
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Definite form may refer to: Definite quadratic form in mathematics Definiteness in linguistics This disambiguation page lists articles associated with...
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isotropic quadratic form. If Q has the same sign for all non-zero vectors, it is a definite quadratic form or an anisotropic quadratic form. There is...
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15 and 290 theorems (category Quadratic forms)
Conway and W. A. Schneeberger in 1993, states that if a positive definite quadratic form with integer matrix represents all positive integers up to 15,...
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in particular: Negative-definite bilinear form Negative-definite quadratic form Negative-definite matrix Negative-definite function This article includes...
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positive-definite if and only if it is the matrix of a positive-definite quadratic form or Hermitian form. In other words, a matrix is positive-definite if...
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Null vector (redirect from Anisotropic_quadratic_space)
which q(x) = 0. In the theory of real bilinear forms, definite quadratic forms and isotropic quadratic forms are distinct. They are distinguished in that...
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mechanics For the definiteness of forms in multilinear algebra, see Definite quadratic form. Definition (disambiguation) Definitive (disambiguation) Absolutely...
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another name for the antiderivative Indefinite forms in algebra, see definite quadratic forms an indefinite matrix Eternity NaN Undefined (disambiguation) This...
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mathematics, a universal quadratic form is a quadratic form over a ring that represents every element of the ring. A non-singular form over a field which represents...
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a quadratic programming problem is also a quadratic programming problem. To see this let us focus on the case where c = 0 and Q is positive definite. We...
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Pin group (section Definite form)
group is not surjective or a universal covering space, but if the quadratic form is definite (and dimension is greater than 2), it is both. The non-trivial...
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x ) = λ 2 Q ( x ) {\displaystyle Q(Tx)=\lambda ^{2}Q(x)} For a definite quadratic form, the conformal orthogonal group is equal to the orthogonal group...
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quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions...
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of the bilinear form and the quadratic form, and it makes sense to speak of the symmetric bilinear form associated with a quadratic form. When char(K) =...
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Hurwitz's theorem (composition algebras) (category Quadratic forms)
algebras endowed with a nondegenerate positive-definite quadratic form. The theorem states that if the quadratic form defines a homomorphism into the positive...
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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,...
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Isotropic line (category Quadratic forms)
An isotropic line occurs only with an isotropic quadratic form, and never with a definite quadratic form. Using complex geometry, Edmond Laguerre first...
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Parabola (redirect from Derivation of parabolic form)
the positive-definite quadratic form x2 + y2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x2 − y2. Generalizations...
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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...
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Norm (mathematics) (redirect from Quadratic norm)
above. In those cases the norm is a definite quadratic form. In the split algebras the norm is an isotropic quadratic form. For any norm p : X → R {\displaystyle...
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Donaldson's theorem (category Quadratic forms)
{\displaystyle n(Q)} . An elementary argument that applies to any negative definite quadratic form over the integers tells us that n ( Q ) ≤ rank ( Q ) {\displaystyle...
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Positive semidefinite (redirect from Positive semi-definite)
Positive semidefinite matrix Positive semidefinite quadratic form Positive semidefinite bilinear form This disambiguation page lists mathematics articles...
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mathematics, the tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces. If R is a commutative...
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Gauss composition law (category Quadratic forms)
Friedrich Gauss, for performing a binary operation on integral binary quadratic forms (IBQFs). Gauss presented this rule in his Disquisitiones Arithmeticae...
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{\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...
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