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searching for Symmetric bilinear form 40 found (100 total)

alternate case: symmetric bilinear form

Quasi-Frobenius Lie algebra (314 words) [view diff] exact match in snippet view article find links to article

({\mathfrak {g}},[\,\,\,,\,\,\,])} equipped with a nondegenerate skew-symmetric bilinear form β : g × g → k {\displaystyle \beta :{\mathfrak {g}}\times {\mathfrak
Symplectic representation (283 words) [view diff] exact match in snippet view article find links to article
preserves the symplectic form ω. Here ω is a nondegenerate skew symmetric bilinear form ω : V × V → F {\displaystyle \omega \colon V\times V\to \mathbb
Polarization (Lie algebra) (803 words) [view diff] exact match in snippet view article
polarization is the maximal totally isotropic subspace of a certain skew-symmetric bilinear form on a Lie algebra. The notion of polarization plays an important
Symplectic matrix (2,558 words) [view diff] exact match in snippet view article find links to article
space V {\displaystyle V} equipped with a nondegenerate, skew-symmetric bilinear form ω {\displaystyle \omega } called the symplectic form. A symplectic
Surgery obstruction (1,052 words) [view diff] exact match in snippet view article find links to article
K_{k}({\tilde {M}})} . This defines a symmetric bilinear form in case k = 2 l {\displaystyle k=2l} and a skew-symmetric bilinear form in case k = 2 l + 1 {\displaystyle
Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article
R2n diagonalizing the original positive symmetric bilinear form. Thus every positive symmetric bilinear form lies in the orbit of a diagonal form under
Yang–Mills–Higgs equations (468 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \langle \cdot ,\cdot \rangle } is an invariant symmetric bilinear form on the adjoint bundle. This is sometimes written as tr {\displaystyle
Symplectic group (3,109 words) [view diff] exact match in snippet view article find links to article
vector space over the field F which preserve a non-degenerate skew-symmetric bilinear form. Such a vector space is called a symplectic vector space, and the
Witt's theorem (564 words) [view diff] exact match in snippet view article find links to article
different from 2 together with a non-degenerate symmetric or skew-symmetric bilinear form. If f : U → U' is an isometry between two subspaces of V then f
Skew-Hamiltonian matrix (311 words) [view diff] exact match in snippet view article find links to article
matrix is a specific type of matrix that corresponds to a skew-symmetric bilinear form on a symplectic vector space. Let  V {\displaystyle V} be a vector
Outermorphism (1,653 words) [view diff] exact match in snippet view article find links to article
{\displaystyle b} , where ⋅ {\displaystyle \cdot } is the nondegenerate symmetric bilinear form (scalar product of vectors). This results in the property that
Perfect obstruction theory (596 words) [view diff] exact match in snippet view article find links to article
theory is a perfect obstruction theory together with nondegenerate symmetric bilinear form. Example: Let f be a regular function on a smooth variety (or stack)
Hermitian manifold (1,548 words) [view diff] exact match in snippet view article find links to article
{\displaystyle g={1 \over 2}\left(h+{\bar {h}}\right).} The form g is a symmetric bilinear form on TMC, the complexified tangent bundle. Since g is equal to its
Hermitian manifold (1,548 words) [view diff] exact match in snippet view article find links to article
{\displaystyle g={1 \over 2}\left(h+{\bar {h}}\right).} The form g is a symmetric bilinear form on TMC, the complexified tangent bundle. Since g is equal to its
Donaldson's theorem (1,244 words) [view diff] exact match in snippet view article find links to article
diagonalizable. Michael Freedman had previously shown that any unimodular symmetric bilinear form is realized as the intersection form of some closed, oriented four-manifold
Finsler manifold (1,952 words) [view diff] exact match in snippet view article find links to article
at v is positive definite. Here the Hessian of F2 at v is the symmetric bilinear form g v ( X , Y ) := 1 2 ∂ 2 ∂ s ∂ t [ F ( v + s X + t Y ) 2 ] | s
Coxeter complex (1,258 words) [view diff] exact match in snippet view article find links to article
{\displaystyle (e_{s})_{s\in S}} , which is equipped with the symmetric bilinear form B ( e s , e t ) = − cos ⁡ ( π m ( s , t ) ) {\displaystyle B(e_{s}
Vector (mathematics and physics) (2,684 words) [view diff] no match in snippet view article
vector space, a vector space V equipped with a non-degenerate, skew-symmetric, bilinear form Topological vector space, a blend of topological structure with
Fourier transform on finite groups (2,052 words) [view diff] exact match in snippet view article find links to article
{\displaystyle U} associated to a G {\displaystyle G} -invariant symmetric bilinear form as U = A A ∗ {\displaystyle U=AA^{*}} , where ∗ {\displaystyle
Topological Yang–Mills theory (672 words) [view diff] exact match in snippet view article find links to article
real parameter. tr {\displaystyle {\text{tr}}} is an invariant, symmetric bilinear form on g {\displaystyle {\mathfrak {g}}} . It is denoted tr {\displaystyle
Schur's lemma (Riemannian geometry) (2,544 words) [view diff] exact match in snippet view article
d\kappa ={\frac {n}{2}}d\kappa .} Let B {\displaystyle B} be a symmetric bilinear form on an n {\displaystyle n} -dimensional inner product space ( V
Building (mathematics) (3,216 words) [view diff] exact match in snippet view article
with automorphisms of the Dynkin diagram. Taking the standard symmetric bilinear form with orthonormal basis vi, the map sending a lattice to its dual
Virasoro algebra (4,140 words) [view diff] exact match in snippet view article find links to article
universal enveloping algebra. Then the Shapovalov form is the symmetric bilinear form on the Verma module V c , h {\displaystyle {\mathcal {V}}_{c,h}}
Dirac structure (940 words) [view diff] exact match in snippet view article find links to article
{\displaystyle D=D^{\perp }} , where orthogonality is with respect to the symmetric bilinear form on V × V ∗ {\displaystyle V\times V^{*}} given by ⟨ ( u , α )
Simple Lie group (2,379 words) [view diff] exact match in snippet view article find links to article
exceptional groups, the exponent −26 is the signature of an invariant symmetric bilinear form that is negative definite on the maximal compact subgroup. It is
Schwarz triangle (10,933 words) [view diff] exact match in snippet view article find links to article
es, et be a basis for a 3-dimensional real vector space V with symmetric bilinear form Λ such that Λ ( e s , e t ) = − A , Λ ( e t , e r ) = − B , Λ (
Multilinear form (4,632 words) [view diff] no match in snippet view article find links to article
to as a bilinear form. A familiar and important example of a (symmetric) bilinear form is the standard inner product (dot product) of vectors. An important
Inner product space (7,357 words) [view diff] exact match in snippet view article find links to article
an inner product on a real vector space is a positive-definite symmetric bilinear form. The binomial expansion of a square becomes ⟨ x + y , x + y ⟩ =
Heisenberg group (5,924 words) [view diff] exact match in snippet view article find links to article
finite-dimensional real symplectic vector space (so ω is a nondegenerate skew symmetric bilinear form on V). The Heisenberg group H(V) on (V, ω) (or simply V for brevity)
Covariance and contravariance of vectors (7,130 words) [view diff] exact match in snippet view article find links to article
finite-dimensional vector space V over a field K with a non-degenerate symmetric bilinear form g : V × V → K (which may be referred to as the metric tensor),
Glossary of classical algebraic geometry (11,193 words) [view diff] exact match in snippet view article find links to article
projective space of a vector space is essentially a non-degenerate skew-symmetric bilinear form, up to multiplication by scalars. See also polarity. (Semple &
Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article
b_{2})+(b_{1},a_{2})+\beta (T_{1},T_{2}),}} where β(T1,T2) is the symmetric bilinear form defined by β ( R ( a , b ) , R ( c , d ) ) = ( R ( a , b ) c ,
Grassmannian (8,402 words) [view diff] exact match in snippet view article find links to article
\operatorname {SO} (n-k)).} Given a real or complex nondegenerate symmetric bilinear form Q {\displaystyle Q} on the n {\displaystyle n} -dimensional space
W-algebra (5,488 words) [view diff] exact match in snippet view article find links to article
} denotes the Killing form. This induces a non-degenerate anti-symmetric bilinear form on the −1 graded piece by the rule: ω χ ( x , y ) = χ ( [ x , y
Spinor (9,924 words) [view diff] exact match in snippet view article find links to article
be a finite-dimensional complex vector space with nondegenerate symmetric bilinear form g. The Clifford algebra Cℓ(V, g) is the algebra generated by V
Symmetric cone (16,613 words) [view diff] exact match in snippet view article find links to article
adjoint relation L(a*) = L(a)* holds for a in EC. Similarly the symmetric bilinear form β(a,b) = (a,b*) satisfies β(ab,c) = β(b,ac). If the inner product
Derivations of the Lorentz transformations (11,515 words) [view diff] exact match in snippet view article find links to article
p ) {\displaystyle (n,p)} . Suppose g {\displaystyle g} is a symmetric bilinear form on V {\displaystyle V} such that the null set of the associated
Differential geometry of surfaces (17,641 words) [view diff] exact match in snippet view article find links to article
with a Riemannian metric. Note that in some more recent texts the symmetric bilinear form on the right hand side is referred to as the second fundamental
Oscillator representation (21,532 words) [view diff] exact match in snippet view article find links to article
Q ( a + b ) − 1 {\displaystyle (a,b)=Q(a)Q(b)Q(a+b)^{-1}} is a symmetric bilinear form on A that is non-degenerate, so permits an identification between
Lie algebra extension (17,708 words) [view diff] exact match in snippet view article find links to article
model with Lie algebra u(1) ⊕ su(2) ⊕ su(3). The Killing form is a symmetric bilinear form on g defined by K ( G 1 , G 2 ) = t r a c e ( a d G 1 a d G 2 )