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'''Gamas's theorem''' is a result in [[multilinear algebra]] which states the necessary and sufficient conditions for a [[tensor]] sym |journal=Linear Algebra and Its Applications ...

In [[multilinear algebra]], '''mode-m flattening'''{{r|Vasilescu2009|vasilescu2002|eldensavas}}, als This operation is used in tensor algebra and its methods, such as [[Parafac]] and [[HOSVD]].{{cn|date=March 2023}} ...

...x,y,z) = x^2 +4y</math> is not. The [[Degree of a polynomial|degree]] of a multilinear polynomial is the maximum number of distinct variables occurring in any mon ...polynomials can be understood as a [[multilinear map]] (specifically, a [[multilinear form]]) applied to the vectors [1 x], [1 y], etc. The general form can be w ...

...aps,<ref name="pairingSurvey" /> however, the problem of constructing such multilinear<ref name="pairingSurvey"/> maps for <math>n > 2</math> seems much more diff In this case, multilinear maps are mostly known as bilinear maps or pairings, and they are usually de ...

...linear maps|tensor product of linear maps]] to a [[tensor]] is called a '''multilinear multiplication'''. ...book|url=https://www.springer.com/gp/book/9780387902845|title=Multilinear Algebra {{!}} Werner Greub {{!}} Springer|series=Universitext|year=1978|publisher=S ...

...chains are taken to be continuous multilinear alternating forms on the Lie algebra of smooth vector fields where the latter is given the <math>C^{\infty}</mat ...Gel'fand |first=I. M. |last2=Fuks |first2=D. B. |title=Cohomologies of Lie algebra of tangential vector fields of a smooth manifold |journal=Funct Anal Its Ap ...

...lean algebra (structure)|Boolean algebra]]. When the [[two-element Boolean algebra]] is used, the Boolean matrix is called a [[logical matrix]]. (In some con Let ''U'' be a non-trivial Boolean algebra (i.e. with at least two elements). Intersection, union, complementation, an ...

...mathematics)|functions]] <math>V \to k</math>. If we fix a [[Basis (linear algebra)|basis]] for ''V'' and write <math>t_i</math> for its dual basis, then ''k' If ''k'' is infinite, then ''k''[''V''] is the [[symmetric algebra]] of the dual space <math>V^*</math>. ...

...ing''' if there is, for some ''N'' > 0, an element ''P'' ≠ 0 of the [[free algebra]], '''Z'''{{angle bracket|''X''₁, ''X''₂, ..., ''X''< ...ee algebra over any ring ''S'' may be used, and gives the concept of '''PI-algebra'''. ...

{{Short description|Process in algebra}} ...{{cite journal|first1=MAO|last1=Vasilescu|first2=D|last2=Terzopoulos|title=Multilinear (tensor) image synthesis, analysis, and recognition [exploratory dsp]|journ ...

In [[multilinear algebra]], a '''reshaping''' of [[Tensor (intrinsic definition)#Definition via tens ...of the <math>M</math> vector spaces <math>V_m</math> has a [[basis (linear algebra)|basis]] <math>\{ v_1^m, v_2^m, \ldots, v_{I_m}^m \}</math>. The expressio ...

|title = A Multilinear Singular Value Decomposition }}</ref> (HOSVD) in [[tensor algebra]], Baranyi and Yam proposed the concept of '''HOSVD-based [[canonical form] ...

...'R'', define <math>\underline{\mathrm{Hom}}(M,N)</math> to be the set of [[Multilinear map|''R''-linear maps]] from ''M'' to ''N'' modulo the relation that ''f''& ...\colon P \to M</math>. Then set <math>\Omega(M)</math> to be the [[Kernel (algebra)|kernel]] of ''p''. Suppose we are given a morphism <math>f \colon M \to N< ...

...roduct]] (informally ''wedge product'') of 1-vectors, and is of ''[[Graded algebra|grade]]'' {{math|''k''}}. ...ion and classification |author=Marcos A. Rodrigues |chapter=§1.2 Geometric algebra: an outline |chapter-url=https://books.google.com/books?id=QbFSt0SlDjIC&pg= ...

...]] over a [[commutative ring]] <math>k</math>, Yang–Baxter operators are [[multilinear mapping|<math>k</math>-linear mappings]] <math>R: V \otimes_k V \rightarrow * [[Hopf algebra]] ...

..._1) = CF (L_0,L_1)</math>. Its finer structure can be described as an [[A∞-algebra|''A''_∞-category]]. ...] conjecture of [[Maxim Kontsevich]].<ref>Kontsevich, Maxim, ''Homological algebra of mirror symmetry'', Proceedings of the International Congress of Mathemat ...

...ra''' is a list of definitions and terms relevant to the field of [[linear algebra]], the branch of mathematics concerned with linear equations and their repr {{term|1=basis|2=[[Basis (linear algebra)|basis]]}} ...

...0895479896305696|issn=0895-4798|citeseerx=10.1.1.102.9135}}</ref> in their Multilinear SVD work that employs the power method, or advocated by Vasilescu and Terzo ...cu, D. Terzopoulos (2005) [http://www.media.mit.edu/~maov/mica/mica05.pdf "Multilinear Independent Component Analysis"], "Proceedings of the IEEE Conference on Co ...

...nar''') is a [[vector space]] ''V'' over a field '''F''' together with a [[multilinear map|'''F'''-trilinear map]] ...rticular, any [[Lie algebra]] defines a Lie triple system and any [[Jordan algebra]] defines a Jordan triple system. They are important in the theories of [[s ...

|journal = Linear Algebra and Its Applications |journal = Linear Algebra and Its Applications ...