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Longer titles found: Degenerate bilinear form (view), Symmetric bilinear form (view), Strongly positive bilinear form (view)

searching for Bilinear form 86 found (273 total)

alternate case: bilinear form

Integral linear operator (2,122 words) [view diff] exact match in snippet view article find links to article

An integral bilinear form is a bilinear functional that belongs to the continuous dual space of X ⊗ ^ ϵ Y {\displaystyle X{\widehat {\otimes }}_{\epsilon

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 , v ) = g (

finite-dimensional vector spaces with a nondegenerate bilinear form, and maps linear transforms that respect the bilinear form, by construction has a natural isomorphism

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 {F}

vector space, which is a vector space with a nondegenerate alternating bilinear form ω {\displaystyle \omega } , such that ω ( e i , e j ) = 0 = ω ( f i

symmetric group and the Hecke-algebras of type A. There is a canonical bilinear form ϕ λ : W ( λ ) × W ( λ ) → R {\displaystyle \phi _{\lambda }:W(\lambda

See also: Glossary of functional analysis. Bra–ket notation Definite bilinear form Direct integral Euclidean space Fundamental theorem of Hilbert spaces

canonical bilinear form B Λ ∈ B i ( X , Y ′ ) , {\displaystyle B_{\Lambda }\in Bi\left(X,Y^{\prime }\right),} called the associated bilinear form on X ×

nondegenerate bilinear form such as the Euclidean dot product or another real inner product. In this case, the nondegenerate bilinear form is often used

}Y} if and only if every bounded bilinear form on E × F {\displaystyle E\times F} extends to a continuous bilinear form on X × Y {\displaystyle X\times

function (an approximate solution) that satisfy the weak statement. The bilinear form uses gradient of the functions that has only 1st order differentiation

an invertible sheaf on the abelian variety, although the associated bilinear form depends only on the image of L {\displaystyle L} in the Néron–Severi

{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

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

{\displaystyle q\geq 3} . The Dolgachev surfaces are simply connected, and the bilinear form on the second cohomology group is odd of signature ( 1 , 9 ) {\displaystyle

)_{L}} where ω {\displaystyle \omega } is a non-degenerate alternating bilinear form defined over K {\displaystyle K} . The second cohomology group describes

D=D^{\perp }} , where orthogonality is with respect to the symmetric bilinear form on V × V ∗ {\displaystyle V\times V^{*}} given by ⟨ ( u , α ) , ( v

structure for the spinor representation, and the type of invariant bilinear form on the spinor representation. The table repeats whenever the dimension

example, doubly even-dimensional manifolds have a symmetric nondegenerate bilinear form on their middle-dimension cohomology group, which thus has an integer-valued

{\displaystyle \langle \cdot ,\cdot \rangle } is an invariant symmetric bilinear form on the adjoint bundle. This is sometimes written as tr {\displaystyle

positive entries, or the positive index of inertia, is an invariant of the bilinear form, i.e. it does not depend on the choice of the diagonalizing basis. This

{\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},e_{t})=-\cos

diagonalizing the original positive symmetric bilinear form. Thus every positive symmetric bilinear form lies in the orbit of a diagonal form under the

{\displaystyle {\hat {B}}} to the c , d {\displaystyle c,d} subspace gives a bilinear form with signature ( + , − ) {\displaystyle (+,-)} . Write the affine root

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 conjugate

Hessian matrix of q having nonzero determinant, or to the associated bilinear form b(x,y) = q(x+y) – q(x) – q(y) being nondegenerate. In general, for k

it determines a bilinear vector-valued form on spinors Q(μ, ξ). This bilinear form then transforms tensorially under a reflection or a rotation. The above

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 ( e r

order on the partitions of n. Moreover, if G is an isometry group of a bilinear form, i.e. an orthogonal or symplectic subgroup of SLn, then its nilpotent

space, a vector space V equipped with a non-degenerate, skew-symmetric, bilinear form Topological vector space, a blend of topological structure with the

defines a bilinear form in 2n dimensions, whose kernel has n dimensions. The quotient by this kernel is a nonsingular bilinear form taking values

algebra g {\displaystyle {\mathfrak {g}}} with respect to the invariant bilinear form on g {\displaystyle {\mathfrak {g}}} . This expression generalizes readily

} is exactly g ν {\displaystyle {\mathfrak {g}}_{\nu }} . (iii) The bilinear form ⟨ ν , [ ⋅ , ⋅ ] ⟩ {\displaystyle \langle \nu ,[\cdot ,\cdot ]\rangle

multiplication. Inner product space: an F vector space V with a definite bilinear form V × V → F. Algebraic structures can also coexist with added structure

finite-dimensional complex vector space with nondegenerate symmetric bilinear form g. The Clifford algebra Cℓ(V, g) is the algebra generated by V along

a perfect obstruction theory together with nondegenerate symmetric bilinear form. Example: Let f be a regular function on a smooth variety (or stack)

approach to soliton equations, based on expressing them in an equivalent bilinear form. The term tau function, or τ {\displaystyle \tau } -function, was first

Michael Freedman had previously shown that any unimodular symmetric bilinear form is realized as the intersection form of some closed, oriented four-manifold

system is said to be positive definite (resp. nondegenerate) if the bilinear form on V defined by the trace of Lu,v is positive definite (resp. nondegenerate)

zero indicator is that there is no invariant nondegenerate complex bilinear form on V. Fulton, William; Harris, Joe (1991). Representation theory. A

] , {\displaystyle {\begin{bmatrix}0&1\\1&-n\end{bmatrix}},} so the bilinear form is two dimensional unimodular, and is even or odd depending on whether

and g, find u∈U such that for all w∈V, aΩ​(w,u)=LΩ​(w) where aΩ is a bilinear form, and LΩ is a linear functional. In S-FEM, the trial solution u and test

{\displaystyle B_{\theta }(X,Y):=-B(X,\theta Y)} is a positive definite bilinear form. Two involutions θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle

Gustavus; Sweedler, Moss Eisenberg (1969). "An associative orthogonal bilinear form for Hopf algebras". Amer. J. Math. 91 (1): 75–94. doi:10.2307/2373270

{B}}_{c}(U)} be the space of hyperfunctions with compact support. Via the bilinear form { B c ( U ) × O ( U ) → C ( f , φ ) ↦ ∫ f ⋅ φ {\displaystyle {\begin{cases}{\mathcal

where we have defined the Stokes operator A {\displaystyle A} and the bilinear form B {\displaystyle B} by A u = − P ( Δ u ) B ( u , v ) = P [ ( u ⋅ ∇ )

{\mathfrak {osp}}(m|2n)} . Consider an even, non-degenerate, supersymmetric bilinear form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } on C m | 2 n

product. The key observation is that W is a symplectic vector space whose bilinear form is obtained from the product of the forms on the tensor factors. Moreover

the dual of a Hilbert space Sesquilinear form – Generalization of a bilinear form Time reversal – Time reversal symmetry in physics Birkenhake, Christina

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 , d ) =

\operatorname {SO} (n-k)).} Given a real or complex nondegenerate symmetric bilinear form Q {\displaystyle Q} on the n {\displaystyle n} -dimensional space V

7-dimensional vector space over the field with 32n+1 elements preserving a bilinear form, a trilinear form, and a product satisfying a twisted linearity law

algebra g {\displaystyle {\mathfrak {g}}} is a symmetric, associative, bilinear form defined by κ ( x , y ) := Tr ( ad x ad y )   ∀ x , y ∈ g {\displaystyle

decomposition. Inner product space: an F vector space V with a definite bilinear form V × V → F. Bialgebra: an associative algebra with a compatible coalgebra

C). This isomorphism is constructed so as to preserve a symplectic bilinear form on C2, that is, to leave the form invariant under Lorentz transformations

groups, the exponent −26 is the signature of an invariant symmetric bilinear form that is negative definite on the maximal compact subgroup. It is equal

ISBN 978-0-19-967677-4. Hirota, R. (1986). "Reduction of soliton equations in bilinear form". Physica D: Nonlinear Phenomena. 18 (1–3): 161–170. Bibcode:1986PhyD

automorphisms of the Dynkin diagram. Taking the standard symmetric bilinear form with orthonormal basis vi, the map sending a lattice to its dual lattice

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 , g )

steps: One begins with a vertex operator algebra V with an invariant bilinear form, an action of M by automorphisms, and with known decomposition of the

projective space of a vector space is essentially the same as a nonsingular bilinear form on the vector space, up to multiplication by constants. (Semple & Roth

the Hadamard product M ∘ N {\displaystyle M\circ N} considered as a bilinear form acts on vectors a , b {\displaystyle a,b} as a ∗ ( M ∘ N ) b = tr ⁡

for a Euclidean Jordan algebra, the real trace defines a symmetric bilinear form with (X, X) = Σ ‖xij‖2. So it is an inner product. It satisfies the

:H_{c}^{2N}(X,\mu _{n}^{N})\rightarrow \mathbf {Z} /n\mathbf {Z} } and the bilinear form Tr(a ∪ b) with values in Z/nZ identifies each of the groups H c i (

Riemannian spaces include compact flat manifolds and nilmanifolds. A natural bilinear form on g {\displaystyle {\mathfrak {g}}} is given by the Killing form. If

parameter. tr {\displaystyle {\text{tr}}} is an invariant, symmetric bilinear form on g {\displaystyle {\mathfrak {g}}} . It is denoted tr {\displaystyle

matrix), when m = 1 {\displaystyle m=1} (a bilinear map is a bilinear form), the bilinear form f ″ ( x ) {\displaystyle f''(x)} is represented by a matrix

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

T_{\xi }^{*}TM} is the Hilbert-form associated with the Lagrangian. The bilinear form g ξ = g i j ( x , ξ ) ( d x i ⊗ d x j ) | x {\displaystyle g_{\xi }=g_{ij}(x

no reasonable notion of a multilinear form (existence of a nonzero bilinear form[clarify] with a regular element of R as value on some pair of arguments

Corollary Let L:'g × g: → F be a non-degenerate symmetric associative bilinear form and let d be a derivation satisfying L ( d ( G 1 ) , G 2 ) = − L ( G

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 an integral

group of U acting on the fiber of Ek at a point. The fiber of E has a bilinear form induced by cup product, which is antisymmetric if d is even, and makes

complexification. However, the transformation required to bring the bilinear form to the complex canonical form is not a Lorentz transformation and hence

L} is a general elliptic operator, the same reasoning leads to the bilinear form A ( u , φ ) = ∫ Ω ∇ u T a ∇ φ − ∫ Ω b T ∇ u φ − ∫ Ω c u φ {\displaystyle

forms Q over the field of 3 elements such that the discriminant of the bilinear form (a,b)=Q(a+b)−Q(a)−Q(b) is ±1. The group Onμ,σ(3), where μ and σ are

{\displaystyle \langle u{\bar {u}}\rangle _{S},} which is not a definite bilinear form and can be equal to zero even if the paravector is not equal to zero

Bini, D.; Lotti, G.; Romani, F. (1980). "Approximate solutions for the bilinear form computational problem". SIAM Journal on Scientific Computing. 9 (4):

gives rise to a left R-linear map, to a right R-linear map, and to an R-bilinear form. Unlike the commutative case, in the general case the tensor product

vector Zoll surface Note that in some more recent texts the symmetric bilinear form on the right hand side is referred to as the second fundamental form;

is a skew-symmetric matrix. It is used to define a symplectic bilinear form on C 2 . {\displaystyle \mathbb {C} ^{2}.} Writing a pair of arbitrary

"On the Camassa–Holm equation and a direct method of solution. I. Bilinear form and solitary waves", Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci

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 comes

+ 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 A

v\in {\mathcal {V}}} , being a ( v , u ) {\displaystyle a(v,u)} the bilinear form satisfying a ( v , u ) = ( v , L u ) {\displaystyle a(v,u)=(v,{\mathcal

0(Ω) ⊆ H ⊆ H1(Ω). A Dirichlet form for Δ given by a bounded Hermitian bilinear form D( f, g) defined for f, g ∈ H1(Ω) such that D( f, g) = (∆f, g) for f