quadratic form
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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
quadratic form — kvadratinis pavidalas statusas T sritis fizika atitikmenys: angl. quadratic form; quadric form vok. quadratische Form, f rus. квадратичная форма, f pranc. forme quadratique, f … Fizikos terminų žodynas
quadratic form — noun : a homogeneous polynomial of the second degree x2 + 5xy + y2 is a quadratic form * * * Math. a polynomial all of whose terms are of degree 2 in two or more variables, as 5x2 2xy + 3y2. [1855 60] … Useful english dictionary
Quadratic form (statistics) — If epsilon is a vector of n random variables, and Lambda is an n dimensional symmetric square matrix, then the scalar quantity epsilon Lambdaepsilon is known as a quadratic form in epsilon. ExpectationIt can be shown that:operatorname{E}left… … Wikipedia
quadratic form — noun Date: 1853 a homogeneous polynomial (as x2 + 5xy + y2) of the second degree … New Collegiate Dictionary
quadratic form — Math. a polynomial all of whose terms are of degree 2 in two or more variables, as 5x2 2xy + 3y2. [1855 60] * * * … Universalium
Ε-quadratic form — In mathematics, specifically the theory of quadratic forms, an ε quadratic form is a generalization of quadratic forms to skew symmetric settings and to * rings; epsilon = pm 1, accordingly for symmetric or skew symmetric. They are also called (… … Wikipedia
Binary quadratic form — In mathematics, a binary quadratic form is a quadratic form in two variables. More concretely, it is a homogeneous polynomial of degree 2 in two variables where a, b, c are the coefficients. Properties of binary quadratic forms depend in an… … 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
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
Hasse invariant of a quadratic form — In mathematics, the Hasse invariant (or Hasse Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br( K ).The quadratic form Q may be taken as a diagonal form: Sigma; a i x i 2.Its invariant is then defined as… … Wikipedia
