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...tinuity but stronger than [[separate continuity]]. Many important bilinear maps that are not continuous are, in fact, hypocontinuous. ...ath>Y</math> and <math>Z</math> are [[topological vector space]]s then a [[bilinear map]] <math>\beta: X\times Y\to Z</math> is called ''hypocontinuous'' if th ...

* {{annotated link|Degenerate bilinear form}} * {{annotated link|Topologies on spaces of linear maps}} ...

...continuous linear operator that arises in a canonical way from an integral bilinear form. These maps play an important role in the theory of [[nuclear space]]s and [[nuclear ma ...

In [[mathematics]], a '''paraproduct''' is a [[non-commutative]] [[bilinear operator]] acting on [[function (mathematics)|functions]] that in some sens [[Category:Bilinear maps]] ...

...r, the problem of constructing such multilinear<ref name="pairingSurvey"/> maps for <math>n > 2</math> seems much more difficult<ref name="bonehMultilinear In this case, multilinear maps are mostly known as bilinear maps or pairings, and they are usually defined as follows:<ref name="KoblitzMene ...

...to the ''continuous'' bilinear maps is the space of ''continuous'' linear maps <math>X \otimes_\pi Y \to Z</math>. .../math> and <math>u_2 : X_2 \to Y_2</math>, their tensor product (as linear maps) <math>u_1 \otimes u_2 : X_1 \otimes_\pi X_2 \to Y_1 \otimes_\pi Y_2</math> ...

...ments separately is called a '''bi-additive map''' or a '''<math>\Z</math>-bilinear map'''.{{refn|{{citation|author=N. Bourbaki|title=Algebra Chapters 1–3|year Typical examples include maps between [[Ring (mathematics)|ring]]s, [[vector space]]s, or [[Module (mathe ...

...set of [[continuous linear map]]s <math>X \to Z</math> (resp. continuous [[bilinear map]]s <math>X \times Y \to Z</math>) will be denoted by <math>L(X; Z)</mat .../math> is the coarsest topology on <math>X^{\prime}</math> making all such maps continuous. ...

...a variety of [[Topology (structure)|topologies]]. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article [[operator topologies]] discusses topologies on spaces of linear maps between [[normed space]]s, whereas this article discusses topologies on suc ...

...habbabi |first1=Fadil |last2=Mbekhta |first2=Mostafa |title=Jordan product maps commuting with the λ-Aluthge transform |journal=Journal of Mathematical Ana [[Category:Bilinear forms]] ...

...Zade|author3-link=Sabir Gusein-Zade| title=Singularities of differentiable maps. Vol. I. The classification of critical points, caustics and wave fronts| t ...[[Signature of a quadratic form|signature]] of a certain non-degenerate [[bilinear form]] (to be defined below) on the local algebra ''B_X''.<ref na ...

...le tensor <math>x \otimes y</math> in <math>X \otimes Y</math>, there is a bilinear map <math>f\in B\left(X^\prime_\sigma, Y^\prime_\sigma\right)</math>, given ...enote the respective dual spaces with the [[Topologies on spaces of linear maps#Topology of bounded convergence|topology of bounded convergence]]. If <math ...

* The set of continuous linear maps ''X'' → ''Z'' (resp. continuous bilinear maps <math>X \times Y \to Z</math>) will be denoted by L(''X'', ''Z'') (resp. B( ...a(x_0)</math>. ''σ''(X′, X) is the coarsest topology on X′ making all such maps continuous. ...

so that the space of linear maps span {L_''u'',''v'':''u'',''v'' ∈ ''V''} is closed under commutat ...m is said to be '''positive definite''' (resp. '''nondegenerate''') if the bilinear form on ''V'' defined by the trace of L_''u'',''v'' is positive d ...

...or space]]s <math>X \to Y</math> and so also to the analysis of TVS-valued maps from [[Euclidean space]]s, which is the focus of this article. ...denote the vector subspace of <math>C^k(\Omega;Y)</math> consisting of all maps in <math>C^k(\Omega;Y)</math> that have compact support. ...

...s equipped with a map to <math>\mathbf{L}_X^\bullet</math> coming from the maps <math>g^*\mathbf{L}_Y^\bullet \to \mathbf{L}_X^\bullet</math> and <math>j^* ...y''' is a perfect obstruction theory together with nondegenerate symmetric bilinear form. ...

...math>\mathbb{K}</math> and a non-[[Degenerate bilinear form|degenerate]] [[bilinear map]] <math>b : X \times Y \to \mathbb{K}</math>. ...pp=225-273}} or more simply called the pairing's <em>map</em> or its <em>[[bilinear form]]</em>. The examples here only describe when <math>\mathbb{K}</math> i ...

...ust not be confused with the tensor product ⊗, which is used to define the bilinear multiplication operator of the tensor algebra. The two act in different spa ...where ''V''^&lowast; denotes the [[dual vector space]] of linear maps ''V'' → '''F'''. It can be turned into a bialgebra with the product <math>v ...

=== Tangent maps === Given a [[nondegenerate bilinear form]] <math> g_p( \cdot , \cdot ) </math> on each <math> T_p M </math> tha ...

...ubgroup of the structure group ''G'' generated by the invertible quadratic maps is the ''inner structure group'' of the J-structure. It is a closed connec ...[[quadratic form]] on the vector space ''V'' over ''K'' with associated [[bilinear form]] ''Q''(''x'',''y'') = ''Q''(''x''+''y'') − ''Q''(''x'') − ''Q''(''y'' ...