- bilinear forms
- • билинейна форма
English-Bulgarian polytechnical dictionary . 2013.
bilinear forms
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Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + … Wikipedia
Bilinear map — In mathematics, a bilinear map is a function of two arguments that is linear in each. An example of such a map is multiplication of integers.DefinitionLet V , W and X be three vector spaces over the same base field F . A bilinear map is a… … Wikipedia
Symmetric bilinear form — A symmetric bilinear form is, as the name implies, a bilinear form on a vector space that is symmetric. They are of great importance in the study of orthogonal polarities and quadrics.They are also more briefly referred to as symmetric forms when … 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
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
Sesquilinear form — In mathematics, a sesquilinear form on a complex vector space V is a map V times; V rarr; C that is linear in one argument and antilinear in the other. The name originates from the numerical prefix meaning one and a half . Compare with a bilinear … Wikipedia
Spin representation — In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are… … Wikipedia
Dual space — In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors… … Wikipedia
Degenerate form — For other uses, see Degeneracy. In mathematics, specifically linear algebra, a degenerate bilinear form ƒ(x,y) on a vector space V is one such that the map from V to V * (the dual space of V) given by is not an isomorphism. An equivalent… … Wikipedia
Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia
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
