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Topic: Multilinear algebra

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	Michael Tsatsomeros' CV
		Linear and Multilinear Algebra, 50 : 151-165, 2002.
		Linear and Multilinear Algebra, 45 : 75-97, 1998.
		Linear and Multilinear Algebra, 41 : 199-210, 1996.
	www.sci.wsu.edu /math/faculty/tsat/cv.html (886 words)

	Publications of Russell Merris
		Grone, Linear & Multilinear Algebra 39 (1995), 133-136.
		Bapat, Linear & Multilinear Algebra 42 (1997), 159-167.
		Lorenzini, Linear & Multilinear Algebra 47 (2000), 281-306.
	www.sci.csuhayward.edu /~rmerris/93.html (873 words)

	Multilinear map - Wikipedia, the free encyclopedia
		In linear algebra, a multilinear map is a mathematical function of several vector variables that is linear in each variable.
		The determinant of a matrix is a skew-symmetric multilinear function of the columns (or rows) of a square matrix.
		The trace of a matrix is a multilinear function of the columns (or rows) of a square matrix.
	en.wikipedia.org /wiki/Multilinear (329 words)

	Chi-Kwong Li: List of Publications and Preprints
		{7.} The $c$-spectral, $c$-radial and $c$-convex matrices, Linear and Multilinear Algebra 20 (1986), 5-15.
		{15.} The $C$-convex matrices, Linear and Multilinear Algebra 21 (1987), 303-312.
		Poon), Linear and Multilinear Algebra 50 (2002), 321-326.
	www.math.wm.edu /~ckli/pub.html (4187 words)

	Linear algebra
		Linear algebra is the branch of mathematics concerned with the study of vectorss, vector spaces (or linear spaces), linear transformations, and systems of linear equations.
		Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis.
		In multilinear algebra one deals with the 'several variables' problem of mappings linear in each of a number of different variables, inevitably leading to the tensor concept.
	www.knowledgefun.com /book/l/li/linear_algebra_1.html (797 words)

	Tufts University \| Computer Science Department -- Colloquia >> Colloquia
		I will present two multilinear models that learn (nonlinear) manifold representations of image ensembles in which the multiple constituent factors (or modes) are disentangled and analyzed explicitly.
		In graphics, our image-based rendering technique, called TensorTextures, is a multilinear generative model that, from a sparse set of example images of a surface, learns the interaction between viewpoint, illumination and geometry, which determines surface appearance, including complex details such as self-occlusion and self shadowing.
		Our tensor algebraic framework is also applicable to human motion data, in order to extract "human motion signatures" that are useful in graphical animation synthesis and motion recognition.
	www.cs.tufts.edu /colloquia/colloquia.php?event=278 (509 words)

	Daniel Hershkowitz -- Selected Publications
		Hershkowitz and A. Berman, Necessary conditions and a sufficient condition for the Fischer Hadamard inequalities, Linear and Multilinear Algebra 13 (1983), 67-72.
		Hershkowitz, Lyapunov diagonal semistability of acyclic matrices, Linear and Multilinear Algebra 22 (1988), 267-283.
		Hershkowitz and F. Shmidel, On a conjecture on the eigenvalues of P-matrices, Linear and Multilinear Algebra 36 (1993), 103-110.
	www.math.technion.ac.il /people/hershkow/index_3.html (1637 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Newsgroups: sci.math Subject: Re: Multilinear alg sources Date: Mon, 2 Mar 1998 01:27:53 -0800 On 2 Mar 1998, ortiz wrote: > Hi > While mathematical litterature on linear algebra abounds in books, few > references are devoted to multilinear algebra (i mean topics like tensor > products, tensor algebra and especially symmetric and exterior algebras).
		Praslov, Problems and Theorems in Linear Algebra (has a long chapter on multilinear algebra and is more readable) If you are ready for multilinear algebra over a module, try D.
		The elementary introduction for multilinear functions is given however in David Hestenes: "New Foundations for Classical Mechanics" (Reidel, 1986), together with an introduction to geometric algebra with many applications in classical mechanics, as the title implies.
	www.math.niu.edu /~rusin/known-math/98/multilin_alg (358 words)

	PlanetMath: Clifford algebra (Site not responding. Last check: 2007-10-08)
		In this case, the algebra is generated by
		Cross-references: quaternions, complex numbers, identity, generated by, algebra, orthonormal basis, inner product, exterior algebra, graded algebra, filtered algebra, filtration, superalgebra, homogeneous, relations, tensor algebra, quotient, symmetric bilinear form, field, vector space
		This is version 6 of Clifford algebra, born on 2002-12-21, modified 2005-10-19.
	planetmath.org /encyclopedia/CliffordAlgebra2.html (159 words)

	Publications of Mathematics Faculty with Undergraduates
		Johnson, and J. Tart, Characterization of Supercommuting Matrices, Linear and Multilinear* Algebra 43 (1997), 35-51.
		C.K. Li, Isometries for the Vector (p,q) and Induced (p,q) Norms, Linear and Multilinear Algebra 38 (1995), 315-332.
		Stanford, Semipositivity of matrices, Linear and Multilinear Algebra 37 (1994), 265-271.
	www.math.wm.edu /~klsmit/udres.html (1276 words)

	http://www.sci.csuhayward.edu/~rmerris
		Ideally suited for a fourth year undergraduate "capstone" course, Multilinear Algebra is also an attractive choice for a beginning graduate course and/or as a research reference.
		Apart from applications to graph theory and the "excursion" into invariant theory, the use of Schur functions as a unifying vehicle in the final chapter may be of particular interest to combinatorialists.
		Purificao Coelho, Linear preserves of the permanent on symmetric matrices, Linear & Multilinear Algebra 41 (1996), 1-8.
	www.mcs.csuhayward.edu /~merris/mla.html (1020 words)

	PlanetMath: tensor algebra (Site not responding. Last check: 2007-10-08)
		From the point of view of category theory, one can describe the tensor algebra construction as a functor
		Cross-references: homomorphism, algebras, forgetful functor, category, functor, category theory, right, bimodule, module, non-commutative, ground ring, cover, tensor product, power, tensor, component, commutative ring
		This is version 7 of tensor algebra, born on 2002-12-18, modified 2005-09-30.
	planetmath.org /encyclopedia/TensorAlgebra.html (94 words)

	The Math Forum - Math Library - Multilinear Algebra
		Linear and Multilinear Algebra; Matrix Theory (Finite and Infinite) - Dave Rusin; The Mathematical Atlas
		Mgfun is a group of Maple packages intended for calculations with multivariate generating functions, in particular for their symbolic summation and integration, and for the proof of special function and combinatorial identities.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/topics/multilinear (305 words)

	[No title]
		Algebra - Mathematical Abstraction from Concrete Experience - Illustrates how the student learns algebra while interacting with manipulatives, physical objects, represented by the numerals and variables of mathematics.
		Algebra is Arithmetic Backwards - For inheritance, fiduciaries, measures, optimization, topology, history, life, and all "backward" projects (for predicting or planning the future from the past).
		Nonassociative Rings and Algebras - Widens scope of rings to be studied, with emphasis on special cases of such rings such as Lie algebras and Jordan algebras.
	botw.org /new/Science/08222005.cfm (1901 words)

	No Title
		A note on pairs of matrices with rank one commutator, Linear and Multilinear Algebra 8 (1979), 97-99.
		An identity of Schur, Linear and Multilinear Algebra 12 (1983), 281-284.
		The rank of a commutator (with C. Lanski), Linear and Multilinear Algebra 13(1983), 167-175.
	www-rcf.usc.edu /~guralnic/Research (1484 words)

	Home page for S. K. Jain
		Group algebras in which the complements are direct summands.
		Nonnegative rank factorization of a nonnegative matrix with AA ≥ 0, Linear and Multilinear Algebra, 51 (2003), 83-95.(with John Tynan).
		3.Nonnegative rank factorization of a nonnegative matrix with AA ≥ 0, Linear and Multilinear Algebra, 51 (2003), 83-95 (with John Tynan).
	www.math.ohiou.edu /~jain (2238 words)

	Havlicek/Multilinear Algebra (Site not responding. Last check: 2007-10-08)
		Multilinear mappings of vector spaces, Existence and universal property of the tensor product, Commutativity and associativity of the tensor product, The tensor product in terms of coordinates, Tensor products and spaces of linear mappings, Kronecker product of linear mappings (matrices), Contraction, Lowering and raising of indices, Duality.
		Covariant, contravariant and mixed tensors, Classical definition and notation of a tensor in terms of coordinates, Structure tensor of an algebra, Mixed tensor algebra, Universal property of the tensor algebra.
		Quadratic forms, Clifford mappings, Cifford mappings and Exterior Algebra, Clifford Algebras, Dimension of a Clifford Algebra, Examples of Clifford Algebras, Structures on a Clifford Algebra.
	www.geometrie.tuwien.ac.at /havlicek/multilineare.html (179 words)

	Research - M. Alex O. Vasilescu
		In this context, we also address an issue fundamental to the multilinear framework for recognition, the inference of mode labels (person, viewpoint, illumination, expression, etc.) of an unlabeled test image.
		Mathematically, TensorTextures is a nonlinear model of texture image ensembles that exploits tensor algebra and the N-mode SVD to learn a representation of the bidirectional texture function (BTF) in which the multiple constituent factors, or modes---viewpoints and illuminations---are disentangled and represented explicitly.
		In addressing this problem, we take advantage of the assets of multilinear algebra, the algebra of higher-order tensors, to obtain a parsimonious representation that separates the various constituent factors.
	www.mrl.nyu.edu /~alex/research_index.html (1146 words)

	Linear Algebra (Site not responding. Last check: 2007-10-08)
		Continuity properties of the Drazin pseudo inverse, Linear Algebra and Its Applications, 10 (1975), 77-83 (with C.D. Meyer, Jr.).
		On the continuity of the Moore-Penrose and Drazin generalized inverses, Linear Algebra and Its Applications, 18 (1977), 53-57.
		Continuity of the Drazin inverse, Linear and Multilinear Alg., 8 (1980), 265-268.
	www4.ncsu.edu /eos/users/s/slc/www/RESEARCH/lin_algebra.html (138 words)

	Amazon.com: Algebra: Books: Saunders MacLane (Site not responding. Last check: 2007-10-08)
		This book presents modern algebra from first principles and is accessible to undergraduates or graduates.
		This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces.
		This jointly written book "Algebra", first published in 1967 and vastly improved in the 3rd Edition, can be far more difficult to tackle unless one goes at it with understanding of how to approach it.
	www.amazon.com /exec/obidos/tg/detail/-/0821816462?v=glance (1921 words)

	Taylor & Francis Journals: Welcome
		This journal publishes original research papers that advance the study of linear and multilinear algebra, or that apply the techniques of linear and multilinear algebra in other branches of mathematics and science.
		spaces over fields or rings, tensor algebras, nonnegative matrices, inequalities in linear algebra, combinatorial matrix theory, numerical linear algebra, representation theory, Lie theory, invariant theory and operator theory.
		The audience for Linear and Multilinear Algebra includes both industrial and academic mathematicians.
	www.tandf.co.uk /journals/titles/03081087.html (116 words)

	Past Paper Page (Site not responding. Last check: 2007-10-08)
		Rank one perturbation and its application to the Laplacian spectrum of a graph, Linear and Multilinear Algebra 46 (1999) 193--198.
		Convexity of the upper complex plane part of the numerical range of a quaternionic matrix, with Robert C. Thompson, Linear and Multilinear Algebra 41 (1996) 303-366.
		Facial structures of Schatten p-norms, Linear and Multilinear Algebra 27 (1990) 207--212.
	www.math.sjsu.edu /~so/pastpaper.html (539 words)

	Items Authored by Uhlig, Frank
		Linear and Multilinear Algebra 46 (1999), no. 4, 327--359.
		Linear and Multilinear Algebra 38 (1994), no. 1-2, 13--37.
		Linear and Multilinear Algebra 36 (1993), no. 1, 69--78.
	www.auburn.edu /~uhligfd/emath_Ju04.html (1004 words)

	Publisher description for Library of Congress control number 83027210 (Site not responding. Last check: 2007-10-08)
		Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion.
		The aim of this book is to provide a readable and systematic account of multilinear algebra at a level suitable for graduate students.
		The volume as a whole is based on advanced lectures given by the author at the University of Sheffield.
	www.loc.gov /catdir/description/cam031/83027210.html (178 words)

	MathGuide - Simple Search (Site not responding. Last check: 2007-10-08)
		Numerical analysis; Linear and multilinear algebra, matrix theory; Ordinary differential equations; Approximations and expansions; Calculus of variations and optimal control, optimization
		Field theory and polynomials; Commutative rings and algebras; Algebraic geometry; Linear and multilinear algebra, matrix theory; Associative rings and algebras; Nonassociative rings and algebras; Category theory, homological algebra
		Linear and multilinear algebra, matrix theory; Partial differential equations; Approximations and expansions; Integral equations; Functional analysis; Calculus of variations and optimal control, optimization; Numerical analysis
	www.mathguide.de /cgi-bin/ssgfi/suche.pl?db=math&tag=SUC&words=15-XX&sort=&dsp=minitemp&COL=SUB (178 words)

	David Carlson
		Co-recipient of an NSF grant for a conference in matrix theory held at Auburn, Alabama, March 1980, which was attended by over 100 participants from the U.S., Canada, and abroad.
		Spectral radius and seminorms in finite dimensional algebras II (with Peter Johnson).
		Cones in the group algebra related to Schur's determinantal inequality (with R. Merris and W. Watkins).
	www-rohan.sdsu.edu /~bobgrone/B_Grone.htm (1164 words)

	Amazon.com: Multilinear Algebra (Algebra, Logic and Applications): Books: Russell Merris (Site not responding. Last check: 2007-10-08)
		Another attraction of multilinear algebra lies in its power to unify such seemingly diverse topics.
		This is done in the final chapter by means of the rational representations of the full linear group.
		Exercises in Algebra: A Collection of Exercises in Algebra, Linear Algebra and Geometry (Algebra, Logic and Applications) by Alexandra I. Kostrikin in Front Matter
	www.amazon.com /exec/obidos/tg/detail/-/9056990780?v=glance (698 words)

	15: Linear and multilinear algebra; matrix theory
		Classic topics in linear algebra and matrix theory are at the center of the diagram: 15A03: Vector spaces, 15A04: Linear transformations, 15A15: Determinants, and 15A21: Canonical forms (e.g.
		At the far right are several large areas of activity in numerical linear algebra and related topics, typically, the study of individual matrices or transformations between (large-dimensional) real vector spaces.
		Furthest down is 15A72: Invariant theory and tensor algebra, which crosses to the study of invariants in Group Theory (20) and in polynomial rings (13: Commutative Algebra and 14: Algebraic Geometry).
	www.math.niu.edu /~rusin/known-math/index/15-XX.html (1605 words)

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