In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements...

In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the...

specifically linear algebra, a degenerate bilinear form f (x, y ) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space...

ordered field. Quadratic forms correspond one-to-one to symmetric bilinear forms over the same space. A symmetric bilinear form is also described as definite...

form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. A bilinear form is...

defines a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y). By defining the transpose of this bilinear form as the bilinear form tB defined...

Thus, bq is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form q ( x ) = b ( x , x ) ,...

\mathbf {Y} )} is called the Killing form; it is used to classify Lie algebras. The trace defines a bilinear form: ( X , Y ) ↦ tr ⁡ ( X Y )   . {\displaystyle...

In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and...

of the bilinear form on the new basis is P T B P . {\displaystyle P^{\mathsf {T}}\mathbf {B} P.} A symmetric bilinear form is a bilinear form B such that...

In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each...

Since it is not positive-definite, this bilinear form is not an inner product; nevertheless the bilinear form is frequently referred to as an indefinite...

field X at 0 is given by the signature of a certain non-degenerate bilinear form (to be defined below) on the local algebra BX. The dimension of B X...

a symplectic bilinear form. A symplectic bilinear form is a mapping ω : V × V → F {\displaystyle \omega :V\times V\to F} that is Bilinear Linear in each...

space V {\displaystyle V} (over any field) equipped with a symmetric bilinear form ⁠ ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } ⁠, where orthogonality...

appropriate indefinite orthogonal group. The quadratic form q gives rise to a symmetric bilinear form defined as follows: ⟨ x , y ⟩ = 1 2 [ q ( x + y ) −...

linear functionals on spaces of test functions. Every non-degenerate bilinear form on a finite-dimensional vector space V induces an isomorphism V → V∗ :...

space. Using the polarization identity the quadratic form is converted to a symmetric bilinear form called the Minkowski inner product, though it is not...

c\|x\|^{2}} for all x {\displaystyle x} in H . {\displaystyle H.} A bilinear form a : H × H → R {\displaystyle a:H\times H\to \mathbb {R} } is called...

{\displaystyle W} of a vector space V {\displaystyle V} equipped with a bilinear form B {\displaystyle B} is the set W ⊥ {\displaystyle W^{\perp }} of all...

A lattice is a free abelian group of finite rank with a symmetric bilinear form (·, ·). The lattice is integral if (·,·) takes integer values. The dimension...

antisymmetrization of a bilinear map are bilinear; thus away from 2, every bilinear form is a sum of a symmetric form and a skew-symmetric form, and there is no...

unweighted bilinear form ⟨ f , g ⟩ := ∫ Ω f ( x ) g ( x )   d x {\displaystyle \langle f,g\rangle :=\int _{\Omega }f(x)g(x)\ dx} to a weighted bilinear form ⟨...

a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors...

the symmetric bilinear form associated with Q, via the polarization identity. Quadratic forms and Clifford algebras in characteristic 2 form an exceptional...

form in the theory of abelian varieties and modular forms, is the following data: A lattice Λ in a complex vector space Cg. An alternating bilinear form...

this context "symmetric bilinear forms" are often referred to as "symmetric forms". These formulas also apply to bilinear forms on modules over a commutative...

(after Walther Ritz) typically assumes symmetric and positive-definite bilinear form in the weak formulation, where the differential equation for a physical...

may be summarized by saying that the dot product is a bilinear form. Moreover, this bilinear form is positive definite, which means that a ⋅ a {\displaystyle...

Look up bilinear in Wiktionary, the free dictionary. Bilinear may refer to: Bilinear sampling (also called "bilinear filtering"), a method in computer...