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تعداد نتایج: 293

Matrix Theory

Basic Results and Techniques

By Fuzhen Zhang
Publisher: Springer Science & Business Media, 2013-03-14
Pages: 290
Language: en
ISBN_13:9781475757972
ISBN_10:1475757972
Subject: Mathematics

Linear Algebra

Challenging Problems for Students

جزئیات و درخواست

By Fuzhen Zhang
Publisher: JHU Press, 1996-08-22
Pages: 192
Language: en
ISBN_10:0801854598
ISBN_13:9780801854590
Subject: Mathematics

Problems In Linear Algebra And Matrix Theory

جزئیات و درخواست

By Fuzhen Zhang
Publisher: World Scientific, 2021-10-25
Pages: 477
Language: en
ISBN_13:9789811239106
ISBN_10:981123910X
Subject: Mathematics

Matrix Theory

جزئیات و درخواست

By Fuzhen Zhang
2014-01-15
Pages: 296
Language: en
ISBN_10:1475757980
ISBN_13:9781475757989

The Schur Complement and Its Applications

جزئیات و درخواست

By Fuzhen Zhang
Publisher: Springer Science & Business Media, 2006-03-30
Pages: 308
Language: en
ISBN_13:9780387242736
ISBN_10:0387242732
Subject: Mathematics

Directory of Chinese Scientific and Educational Officials

Free Epub

جزئیات و درخواست

By National Foreign Assessment Center (U.S.)
1979
Pages: 594
Language: en
OTHER:STANFORD:36105113720937
Subject: China

Separabilität in kommutativen und auflösbaren Algebren. Unter Berücksichtigung nicht-unitärer assoziativer Algebren; mit 241 Übungsaufgaben

جزئیات و درخواست

By Sven Bodo Wirsing
Publisher: disserta Verlag, 2015-09
Pages: 189
Language: de
ISBN_13:9783959351768
ISBN_10:3959351763
Subject: Mathematics

Contributions To Probability And Statistics: Applications And Challenges - Proceedings Of The International Statistics Workshop

جزئیات و درخواست

By Peter Brown, Shuangzhe Liu, Dharmendra Sharma
Publisher: World Scientific, 2006-10-23
Pages: 323
Language: en
ISBN_13:9789814476478
ISBN_10:9814476471
Subject: Mathematics

Micro/Nano Materials for Clean Energy and Environment

جزئیات و درخواست

By Zhongchao Tan, Qinghai Li
Publisher: MDPI, 2019-07-01
Pages: 198
Language: en
ISBN_13:9783039211289
ISBN_10:3039211285
Subject: Technology & Engineering

Don't Tell the Boss!

How Poor Communication on Risks within Organizations Causes ...

جزئیات و درخواست

By Dmitry Chernov, Didier Sornette, Giovanni Sansavini, Ali Ayoub
Publisher: Springer Nature, 2023-01-20
Pages: 493
Language: en
ISBN_13:9783031052064
ISBN_10:3031052064
Subject: Business & Economics

Convex Optimization & Euclidean Distance Geometry

$The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs has already proven invaluable in discerning biological molecular conformation.The emerging practice of localization in wireless sensor networks, the global positioning system (GPS), and distance-based pattern recognitionwill certainly simplify and benefit from this theory.We study the pervasive convex Euclidean bodies and their various representations.In particular, we make convex polyhedra, cones, and dual cones more visceral through illustration, andwe study the geometric relation of polyhedral cones to nonorthogonal bases biorthogonal expansion.We explain conversion between halfspace- and vertex-descriptions of convex cones,we provide formulae for determining dual cones,and we show how classic alternative systems of linear inequalities or linear matrix inequalities and optimality conditions can be explained by generalized inequalities in terms of convex cones and their duals.The conic analogue to linear independence, called conic independence, is introducedas a new tool in the study of classical cone theory; the logical next step in the progression:linear, affine, conic.Any convex optimization problem has geometric interpretation.This is a powerful attraction: the ability to visualize geometry of an optimization problem.We provide tools to make visualization easier.The concept of faces, extreme points, and extreme directions of convex Euclidean bodiesis explained here, crucial to understanding convex optimization.The convex cone of positive semidefinite matrices, in particular, is studied in depth.We mathematically interpret, for example,its inverse image under affine transformation, and we explainhow higher-rank subsets of its boundary united with its interior are convex.The Chapter on "Geometry of convex functions",observes analogies between convex sets and functions:The set of all vector-valued convex functions is a closed convex cone.Included among the examples in this chapter, we show how the real affinefunction relates to convex functions as the hyperplane relates to convex sets.Here, also, pertinent results formultidimensional convex functions are presented that are largely ignored in the literature;tricks and tips for determining their convexityand discerning their geometry, particularly with regard to matrix calculus which remains largely unsystematizedwhen compared with the traditional practice of ordinary calculus.Consequently, we collect some results of matrix differentiation in the appendices.The Euclidean distance matrix (EDM) is studied,its properties and relationship to both positive semidefinite and Gram matrices.We relate the EDM to the four classical axioms of the Euclidean metric;thereby, observing the existence of an infinity of axioms of the Euclidean metric beyondthe triangle inequality. We proceed byderiving the fifth Euclidean axiom and then explain why furthering this endeavoris inefficient because the ensuing criteria (while describing polyhedra)grow linearly in complexity and number.Some geometrical problems solvable via EDMs,EDM problems posed as convex optimization, and methods of solution arepresented;\eg, we generate a recognizable isotonic map of the United States usingonly comparative distance information (no distance information, only distance inequalities).We offer a new proof of the classic Schoenberg criterion, that determines whether a candidate matrix is an EDM. Our proofrelies on fundamental geometry; assuming, any EDM must correspond to a list of points contained in some polyhedron(possibly at its vertices) and vice versa.It is not widely known that the Schoenberg criterion implies nonnegativity of the EDM entries; proved here.We characterize the eigenvalues of an EDM matrix and then devisea polyhedral cone required for determining membership of a candidate matrix(in Cayley-Menger form) to the convex cone of Euclidean distance matrices (EDM cone); \ie,a candidate is an EDM if and only if its eigenspectrum belongs to a spectral cone for EDM^N.We will see spectral cones are not unique.In the chapter "EDM cone", we explain the geometric relationship betweenthe EDM cone, two positive semidefinite cones, and the elliptope.We illustrate geometric requirements, in particular, for projection of a candidate matrixon a positive semidefinite cone that establish its membership to the EDM cone. The faces of the EDM cone are described,but still open is the question whether all its faces are exposed as they are for the positive semidefinite cone.The classic Schoenberg criterion, relating EDM and positive semidefinite cones, isrevealed to be a discretized membership relation (a generalized inequality, a new Farkas''''''''-like lemma)between the EDM cone and its ordinary dual. A matrix criterion for membership to the dual EDM cone is derived thatis simpler than the Schoenberg criterion.We derive a new concise expression for the EDM cone and its dual involvingtwo subspaces and a positive semidefinite cone."Semidefinite programming" is reviewedwith particular attention to optimality conditionsof prototypical primal and dual conic programs,their interplay, and the perturbation method of rank reduction of optimal solutions(extant but not well-known).We show how to solve a ubiquitous platonic combinatorial optimization problem from linear algebra(the optimal Boolean solution x to Ax=b)via semidefinite program relaxation.A three-dimensional polyhedral analogue for the positive semidefinite cone of 3X3 symmetricmatrices is introduced; a tool for visualizing in 6 dimensions.In "EDM proximity"we explore methods of solution to a few fundamental and prevalentEuclidean distance matrix proximity problems; the problem of finding that Euclidean distance matrix closestto a given matrix in the Euclidean sense.We pay particular attention to the problem when compounded with rank minimization.We offer a new geometrical proof of a famous result discovered by Eckart \& Young in 1936 regarding Euclideanprojection of a point on a subset of the positive semidefinite cone comprising all positive semidefinite matriceshaving rank not exceeding a prescribed limit rho.We explain how this problem is transformed to a convex optimization for any rank rho.$

جزئیات و درخواست

By Jon Dattorro
Publisher: Meboo Publishing USA, 2005
Pages: 776
Language: en
ISBN_13:9780976401308
ISBN_10:0976401304
Subject: Mathematics

Matrix Theory

From Generalized Inverses to Jordan Form

جزئیات و درخواست

By Robert Piziak, P.L. Odell
Publisher: CRC Press, 2007-02-22
Pages: 568
Language: en
ISBN_13:9781420009934
ISBN_10:1420009931
Subject: Mathematics

Scalar, Vector, and Matrix Mathematics

Theory, Facts, and Formulas - Revised and Expanded Edition

جزئیات و درخواست

By Dennis S. Bernstein
Publisher: Princeton University Press, 2018-02-27
Pages: 1593
Language: en
ISBN_13:9780691176536
ISBN_10:0691176531
Subject: Mathematics

Handbook of Linear Algebra, Second Edition

جزئیات و درخواست

By Leslie Hogben
Publisher: CRC Press, 2013-11-26
Pages: 1906
Language: en
ISBN_13:9781466507289
ISBN_10:1466507284
Subject: Mathematics

Matrix Mathematics

Theory, Facts, and Formulas, Second Edition

جزئیات و درخواست

By Dennis S. Bernstein
Publisher: Princeton University Press, 2009-07-06
Pages: 1184
Language: en
ISBN_13:9781400833344
ISBN_10:1400833345
Subject: Mathematics

The Plague Year

America in the Time of Covid

جزئیات و درخواست

By Lawrence Wright
Publisher: Vintage, 2021-06-08
Pages: 417
Language: en
ISBN_13:9780593320730
ISBN_10:0593320735
Subject: Political Science

Algorithmic Cryptanalysis

جزئیات و درخواست

By Antoine Joux
Publisher: CRC Press, 2009-06-15
Pages: 516
Language: en
ISBN_13:9781420070033
ISBN_10:1420070037
Subject: Computers

Innovations in Multivariate Statistical Analysis

A Festschrift for Heinz Neudecker

جزئیات و درخواست

By Risto D.H. Heijmans, D.S.G. Pollock, Albert Satorra
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 302
Language: en
ISBN_13:9781461546030
ISBN_10:1461546036
Subject: Business & Economics

Maximum-Entropy Sampling

Algorithms and Application

جزئیات و درخواست

By Marcia Fampa, Jon Lee
Publisher: Springer Nature, 2022-11-30
Pages: 206
Language: en
ISBN_13:9783031130786
ISBN_10:3031130782
Subject: Mathematics

Matrix Mathematics

A Second Course in Linear Algebra

جزئیات و درخواست

By Stephan Ramon Garcia, Roger A. Horn
Publisher: Cambridge University Press, 2023-05-25
Pages: 492
Language: en
ISBN_13:9781108945592
ISBN_10:1108945597
Subject: Mathematics

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