Handbook of Linear Algebra

2. New Auflage 2016
ISBN: 978-1-138-19989-7
Verlag: Taylor & Francis Ltd

Buch, Englisch, 1904 Seiten, Format (B × H): 258 mm x 187 mm, Gewicht: 2604 g

Reihe: Discrete Mathematics and Its Applications

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.
New to the Second Edition

Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets
New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems
More chapters on applications of linear algebra, including epidemiology and quantum error correction
New chapter on using the free and open source software system Sage for linear algebra
Additional sections in the chapters on sign pattern matrices and applications to geometry
Conjectures and open problems in most chapters on advanced topics

Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Zielgruppe

Mathematicians, statisticians, engineers, physicists, biologists, economists, and computer scientists.

Autoren/Hrsg.

Hogben, Leslie

Inhaltsverzeichnis

Linear AlgebraLinear AlgebraVectors, Matrices, and Systems of Linear Equations Jane DayLinear Independence, Span, and Bases Mark Mills Linear Transformations Francesco Barioli Determinants and Eigenvalues Luz M. DeAlbaInner Product Spaces, Orthogonal Projection, Least Squares, and Singular Value Decomposition Lixing Han and Michael Neumann Canonical Forms Leslie Hogben Other Canonical Forms Roger A. Horn and Vladimir V. Sergeichuk Unitary Similarity, Normal Matrices, and Spectral Theory Helene ShapiroHermitian and Positive Definite Matrices Wayne Barrett Nonnegative and Stochastic Matrices Uriel G. RothblumPartitioned Matrices Robert Reams

Topics in Linear AlgebraSchur Complements Roger A. Horn and Fuzhen Zhang Quadratic, Bilinear, and Sesquilinear Forms Raphael LoewyMultilinear Algebra J.A. Dias da Silva and Armando Machado Tensors and Hypermatrices Lek-Heng Lim Matrix Equalities and Inequalities Michael Tsatsomeros Functions of Matrices Nicholas J. Higham Matrix Polynomials Jorg Liesen and Christian Mehl Matrix Equations Beatrice MeiniInvariant Subspaces G.W. Stewart Matrix Perturbation Theory Ren-Cang Li Special Types of Matrices Albrecht Bottcher and Ilya Spitkovsky Pseudospectra Mark Embree Singular Values and Singular Value Inequalities Roy Mathias Numerical Range Chi-Kwong Li Matrix Stability and Inertia Daniel Hershkowitz Generalized Inverses of Matrices Yimin WeiInverse Eigenvalue Problems Alberto Borobia Totally Positive and Totally Nonnegative Matrices Shaun M. Fallat Linear Preserver Problems Peter SemrlMatrices over Finite Fields J. D. BothaMatrices over Integral Domains Shmuel Friedland Similarity of Families of Matrices Shmuel Friedland Representations of Quivers and Mixed Graphs Roger A. Horn and Vladimir V. SergeichukMax-Plus Algebra Marianne Akian, Ravindra Bapat, and Stephane Gaubert Matrices Leaving a Cone Invariant Bit-Shun Tam and Hans SchneiderSpectral Sets Catalin Badea and Bernhard Beckermann

Combinatorial Matrix Theory and GraphsCombinatorial Matrix TheoryCombinatorial Matrix Theory Richard A. Brualdi Matrices and Graphs Willem H. Haemers Digraphs and Matrices Jeffrey L. Stuart Bipartite Graphs and Matrices Bryan L. ShaderSign Pattern Matrices Frank J. Hall and Zhongshan Li

Topics in Combinatorial Matrix TheoryPermanents Ian M. Wanless D-Optimal Matrices Michael G. Neubauer and William Watkins Tournaments T.S. Michael Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs Shaun M. Fallat and Leslie HogbenSpectral Graph Theory Steve Butler and Fan ChungAlgebraic Connectivity Steve Kirkland Matrix Completion Problems Luz M. DeAlba, Leslie Hogben, and Amy Wangsness Wehe

Numerical MethodsNumerical Methods for Linear SystemsVector and Matrix Norms, Error Analysis, Efficiency, and Stability Ralph Byers and Biswa Nath Datta Matrix Factorizations and Direct Solution of Linear Systems Christopher BeattieLeast Squares Solution of Linear Systems Per Christian Hansen and Hans Bruun Nielsen Sparse Matrix Methods Esmond G. NgIterative Solution Methods for Linear Systems Anne Greenbaum

Numerical Methods for EigenvaluesSymmetric Matrix Eigenvalue Techniques Ivan Slapnicar Unsymmetric Matrix Eigenvalue Techniques David S. WatkinsThe Implicitly Restarted Arnoldi Method D.C. Sorensen Computation of the Singular Value Decomposition Alan Kaylor Cline and Inderjit S. Dhillon Computing Eigenvalues and Singular Values to High Relative Accuracy Zlatko Drmac Nonlinear Eigenvalue Problems Heinrich Voss

Topics in Numerical Linear AlgebraFast Matrix Multiplication Dario A. Bini Fast Algorithms for Structured Matrix Computations Michael Stewart Structured Eigenvalue Problems Structure-Preserving Algorithms, Structured Error Analysis Heike Fassbender Large-Scale Matrix Computations Roland W. Freund

Linear Algebra in Other DisciplinesApplications to Physical and Biological SciencesLinear Algebra and Mathematical Physics Lorenzo Sadun Linear Algebra in Biomolecular Modeling Zhijun WuLinear Algebra in Mathematical Population Biology and Epidemiology Fred Brauer and Carlos Castillo-Chavez

Applications to OptimizationLinear Programming Leonid N. Vaserstein Semidefinite Programming Henry Wolkowicz

Applications to Probability and StatisticsRandom Vectors and Linear Statistical Models Simo Puntanen and George P.H. Styan Multivariate Statistical Analysis Simo Puntanen, George A.F. Seber, and George P.H. StyanMarkov Chains Beatrice Meini

Applications to Computer ScienceCoding Theory Joachim Rosenthal and Paul Weiner Quantum Computation Zijian Diao Operator Quantum Error Correction Chi-Kwong Li, Yiu-Tung Poon, and Nung-Sing Sze Information Retrieval and Web Search Amy N. Langville and Carl D. Meyer Signal Processing Michael Stewart

Applications to AnalysisDifferential Equations and Stability Volker Mehrmann and Tatjana Stykel Dynamical Systems and Linear Algebra Fritz Colonius and Wolfgang Kliemann Control Theory Peter Benner Fourier Analysis Kenneth Howell

Applications to GeometryGeometry Mark Hunacek Some Applications of Matrices and Graphs in Euclidean Geometry Miroslav Fiedler

Applications to AlgebraMatrix Groups Peter J. Cameron Group Representations Randall R. Holmes and Tin-Yau TamNonassociative Algebras Murray R. Bremner, Lucia I. Murakami, and Ivan P. Shestakov Lie Algebras Robert Wilson

Computational SoftwareInteractive Software for Linear AlgebraMATLAB Steven J. LeonLinear Algebra in Maple David J. Jeffrey and Robert M. Corless Mathematica Heikki Ruskeep’a’a Sage Robert A. Beezer, Robert Bradshaw, Jason Grout, and William Stein

Packages of Subroutines for Linear AlgebraBLAS Jack Dongarra, Victor Eijkhout, and Julien Langou LAPACK Zhaojun Bai, James Demmel, Jack Dongarra, Julien Langou, and Jenny Wang Use of ARPACK and EIGS D.C. Sorensen Summary of Software for Linear Algebra Freely Available on the Web Jack Dongarra, Victor Eijkhout, and Julien Langou

Glossary
Notation Index
Index

Über Autor(innen)

Leslie Hogben is the Dio Lewis Holl Chair in Applied Mathematics and Professor of Mathematics at Iowa State University (ISU), and the Associate Director for Diversity of the American Institute of Mathematics. She received her B.A. from Swarthmore College in 1974 and her Ph. D. in 1978 from Yale University under the direction of Nathan Jacobson. Although originally working in nonassociative algebras, in the mid-1990s, she changed her focus to linear algebra.Dr. Hogben is the author of more than 60 research papers and particularly enjoys introducing students to mathematical research. She has or is advising three postdoctoral associates, 11 doctoral students, 12 master's students, and 30 undergraduate researchers. She is the co-director of the NSF-sponsored ISU Math REU and developed an early graduate research course for mathematics and applied mathematics graduate students at ISU.Dr. Hogben is a frequent co-organizer of meetings, workshops, and special sessions/mini-symposia. She is the Secretary/Treasurer of the International Linear Algebra Society and an associate editor of the journals Linear Algebra and its Applications and Electronic Journal of Linear Algebra.