positive definite quadratic form

正定二次型

English-Chinese computer dictionary (英汉计算机词汇大词典). 2013.

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  • Definite quadratic form — In mathematics, a definite quadratic form is a real valued quadratic form over some vector space V that has the same sign (always positive or always negative) for every nonzero vector of V. The definite quadratic forms correspond in one to one… …   Wikipedia

  • definite quadratic form — noun : a quadratic form that is always positive or always negative for every set of values of the variables involved in it except when all the variables are zero in which case the form has the value zero …   Useful english dictionary

  • 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

  • Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… …   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

  • 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

  • Isotropic quadratic form — In mathematics, a quadratic form over a field F is said to be isotropic if there is a non zero vector on which it evaluates to zero. Otherwise the quadratic form is anisotropic. More precisely, if q is a quadratic form on a vector space V over F …   Wikipedia

  • Quadratic programming — (QP) is a special type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.The quadratic programming problem… …   Wikipedia

  • Binäre quadratische Form — Eine binäre quadratische Form (in diesem Artikel oft kurz nur Form genannt), ist in der Mathematik eine quadratische Form in zwei Variablen x,y, also ein Polynom der Gestalt , wobei a,b,c die Koeffizienten der Form sind. Die Form f mit schreibt… …   Deutsch Wikipedia

  • Quadratically constrained quadratic program — In mathematics, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form: egin{align} ext{minimize} frac12 x^ op P 0 x + q… …   Wikipedia

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