positive definite
adjective Date: 1907 1. having a positive value for all values of the constituent variables <
positive definite quadratic forms
>
2. of a matrix having the characteristic roots real and positive

New Collegiate Dictionary. 2001.

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  • positive definite — positive definiteness. Math. 1. (of a quadratic form) positive for all real values of the variables, where the values are not all zero. 2. (of a matrix) displaying the coefficients of a positive definite quadratic form. [1905 10] * * * …   Universalium

  • Positive definite — In mathematics, positive definite may refer to: * positive definite matrix * positive definite function ** positive definite function on a group * positive definite bilinear form …   Wikipedia

  • positive definite — adjective 1. : having a positive value of all values of the constituent variables positive definite quadratic forms 2. of a matrix : having the characteristic roots real and positive * * * positive definiteness. Math. 1. (of a quadratic form)… …   Useful english dictionary

  • Positive-definite matrix — In linear algebra, a positive definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive definite symmetric bilinear form (or a sesquilinear form in the complex case). The… …   Wikipedia

  • Positive-definite function — In mathematics, the term positive definite function may refer to a couple of different concepts. Contents 1 In dynamical systems 2 In analysis 2.1 Bochner s theorem 2.1.1 Applications …   Wikipedia

  • Positive definite function on a group — In operator theory, a positive definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive definite kernel where the underlying set has… …   Wikipedia

  • Positive definite kernel — In operator theory, a positive definite kernel is a generalization of a positive matrix. Definition Let :{ H n } {n in {mathbb Z be a sequence of (complex) Hilbert spaces and :mathcal{L}(H i, H j)be the bounded operators from Hi to Hj . A map A… …   Wikipedia

  • Positive definiteness — is a property of the following mathematical objects:* Positive definite bilinear form * Positive definite matrix * Positive definite function …   Wikipedia

  • Definite bilinear form — In mathematics, a definite bilinear form is a bilinear form B over some vector space V (with real or complex scalar field) such that the associated quadratic form is definite, that is, has a real value with the same sign (positive or negative)… …   Wikipedia

  • Positive linear functional — In mathematics, especially in functional analysis, a positive linear functional on an ordered vector space ( V , ≤) is a linear functional f on V so that for all positive elements v of V , that is v ge;0, it holds that:f(v)geq 0.In other words, a …   Wikipedia

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