mathematics, 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...

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...

varieties Degenerate bilinear form, a bilinear form on a vector space V whose induced map from V to the dual space of V is not an isomorphism Degenerate distribution...

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 ) ,...

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

vector 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...

finite-dimensional vector space V {\displaystyle V} endowed with a non-degenerate bilinear form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , is canonically...

the phase of light. Spacetime is equipped with an indefinite non-degenerate bilinear form, called the Minkowski metric, the Minkowski norm squared or Minkowski...

inner product (such as the dot product; more generally, a non-degenerate bilinear form), we have an isomorphism V → V ∗ , {\displaystyle V\to V^{*},}...

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...

anticommutation relations in terms of a symplectic and a symmetric non-degenerate bilinear form. In addition, the binary elements in this graded Weyl algebra give...

quadratic form is non-degenerate and has the signature (a, b), then its isotropy index is the minimum of a and b. An important example of an isotropic form over...

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...

the degenerate bilinear form d ( v , w ) = v 1 w 1 + v 2 w 2 + v 3 w 3 . {\displaystyle d(v,w)=v_{1}w_{1}+v_{2}w_{2}+v_{3}w_{3}.} This degenerate scalar...

\mathrm {Vir} } , so V {\displaystyle V} is equipped with a non-degenerate bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} and there is an algebra...

non-degenerate bilinear form on TpM by means of g S ( X p , Y p ) = [ S X p , Y p ] . {\displaystyle g_{S}(X_{p},Y_{p})=[SX_{p},Y_{p}]\,.} This bilinear form...

is a non-degenerate, symmetric bilinear form g : V × V → K  a bilinear form {\displaystyle g:V\times V\rightarrow K{\text{ a bilinear form}}} g ( u ...

homeomorphicPages displaying short descriptions of redirect targets Degenerate bilinear form – Possible x & y for x-E conjugates Dual system Topologies on spaces...

generally, given a non-degenerate symmetric bilinear form or quadratic form on a vector space over a field, the orthogonal group of the form is the group of...

bilinear complexity or rank of a bilinear map is an important concept in the asymptotic complexity of matrix multiplication. The rank of a bilinear map...

finite-dimensional. In this case, such an isomorphism is equivalent to a non-degenerate bilinear form φ : V × V → K {\displaystyle \varphi :V\times V\to K} In this case...

the point p {\displaystyle p} . A metric tensor is a non-degenerate, smooth, symmetric, bilinear map that assigns a real number to pairs of tangent vectors...

represent 4 reflections. Let (V, b) be an n-dimensional, non-degenerate symmetric bilinear space over a field with characteristic not equal to 2. Then...

follows. Given a module M over a *-ring R, let B(M) be the space of bilinear forms on M, and let T : B(M) → B(M) be the "conjugate transpose" involution...

{\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...

easy and standard (uses the fact that the trace defines a non-degenerate bilinear form). Let A be a finitely generated algebra over a field k that is...

sesquilinearity reduces to bilinearity. Hence an inner product on a real vector space is a positive-definite symmetric bilinear form. The binomial expansion...

non-degenerate invariant symmetric bilinear form. However the converse is false: a Lie algebra with a non-degenerate invariant symmetric bilinear form need...

finite-dimensional real n-space together with a non-degenerate quadratic form q. Such a quadratic form can, given a suitable choice of basis (e1, …, en)...