just symmetric forms when "bilinear" is understood. Symmetric bilinear forms on finite-dimensional vector spaces precisely correspond to symmetric matrices...

We define a bilinear form to be symmetric if B(v, w) = B(w, v) for all v, w in V; alternating if B(v, v) = 0 for all v in V; skew-symmetric or antisymmetric...

skew-symmetric and symmetric bilinear forms coincide since then 1 = −1. In all cases, alternating bilinear forms are a subset of skew-symmetric bilinear forms...

{T}}Ax.} 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...

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...

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...

({\mathfrak {g}},[\,\,\,,\,\,\,])} equipped with a nondegenerate skew-symmetric bilinear form β : g × g → k {\displaystyle \beta :{\mathfrak {g}}\times {\mathfrak...

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

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...

products represent the quadratic form. Through the polarization identity the quadratic form is related to a symmetric bilinear form B(u, v) = ⁠1/4⁠(q(u + v) −...

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

Symmetric form may refer to: Symmetric bilinear form Symmetric sesquilinear form This disambiguation page lists mathematics articles associated with the...

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 invertible...

In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold...

transposition) is performed. See: Skew-symmetric matrix (a matrix A for which AT = −A) Skew-symmetric bilinear form is a bilinear form B such that B(x, y) = −B(y...

finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the...

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 ) −...

P} if the matrix B is symmetric. If the characteristic of the ground field F is not two, then for every symmetric bilinear form there is a basis for which...

n-dimensional symmetric bilinear space can be described as the composition of at most n reflections. The notion of a symmetric bilinear space is a generalization...

n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature (p, q), where n = p + q. It is also called the pseudo-orthogonal...

the Ricci tensor assigns to each tangent space of the manifold a symmetric bilinear form. Broadly, one could analogize the role of the Ricci curvature in...

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

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

Ernst Witt, is an abelian group whose elements are represented by symmetric bilinear forms over the field. Fix a field k of characteristic not equal to 2...

is symmetric if and only if S is symmetric. There is thus a natural one-to-one correspondence between symmetric bilinear forms on TpM and symmetric linear...

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

to be semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on g {\displaystyle {\mathfrak {g}}} defined by the formula...

G-invariant bilinear form on V if and only if ι χ ≠ 0 {\displaystyle \iota \chi \neq 0} There exists a nonzero G-invariant symmetric bilinear form on V if...

a nondegenerate skew-symmetric bilinear form. One could easily choose bases in which J {\displaystyle J} is not skew-symmetric or Ω {\displaystyle \Omega...

metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number...