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)...

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;...

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...

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...

Positive-definite kernel Positive-definite matrix Positive-definite quadratic form Fasshauer, Gregory E. (2011), "Positive definite kernels: Past, present and...

Definite form may refer to: Definite quadratic form in mathematics Definiteness in linguistics This disambiguation page lists articles associated with...

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...

in particular: Negative-definite bilinear form Negative-definite quadratic form Negative-definite matrix Negative-definite function This article includes...

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...

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...

mechanics For the definiteness of forms in multilinear algebra, see Definite quadratic form. Definition (disambiguation) Definitive (disambiguation) Absolutely...

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,...

another name for the antiderivative Indefinite forms in algebra, see definite quadratic forms an indefinite matrix Eternity NaN Undefined (disambiguation) This...

algebras endowed with a nondegenerate positive-definite quadratic form. The theorem states that if the quadratic form defines a homomorphism into the positive...

An isotropic line occurs only with an isotropic quadratic form, and never with a definite quadratic form. Using complex geometry, Edmond Laguerre first...

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...

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) =...

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...

quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions...

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...

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...

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,...

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...

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...

mathematics, Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms. It was proved in 2003 by Irving...

{\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...

the positive-definite quadratic form x2 + y2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x2 − y2. Generalizations...

positive definite even unimodular quadratic form in 8 variables, and conversely such a quadratic form can be used to construct a positive-definite, even...

Positive semidefinite matrix Positive semidefinite quadratic form Positive semidefinite bilinear form This disambiguation page lists mathematics articles...

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...