Handbook of Linear Algebra: (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.

Table of Contents:
Linear Algebra Linear Algebra Vectors, Matrices, and Systems of Linear Equations Jane Day Linear Independence, Span, and Bases Mark Mills Linear Transformations Francesco Barioli Determinants and Eigenvalues Luz M. DeAlba Inner 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 Shapiro Hermitian and Positive Definite Matrices Wayne Barrett Nonnegative and Stochastic Matrices Uriel G. Rothblum Partitioned Matrices Robert Reams Topics in Linear Algebra Schur Complements Roger A. Horn and Fuzhen Zhang Quadratic, Bilinear, and Sesquilinear Forms Raphael Loewy Multilinear 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 Meini Invariant 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 Wei Inverse Eigenvalue Problems Alberto Borobia Totally Positive and Totally Nonnegative Matrices Shaun M. Fallat Linear Preserver Problems Peter Semrl Matrices over Finite Fields J. D. Botha Matrices over Integral Domains Shmuel Friedland Similarity of Families of Matrices Shmuel Friedland Representations of Quivers and Mixed Graphs Roger A. Horn and Vladimir V. Sergeichuk Max-Plus Algebra Marianne Akian, Ravindra Bapat, and Stephane Gaubert Matrices Leaving a Cone Invariant Bit-Shun Tam and Hans Schneider Spectral Sets Catalin Badea and Bernhard Beckermann Combinatorial Matrix Theory and Graphs Combinatorial Matrix Theory Combinatorial Matrix Theory Richard A. Brualdi Matrices and Graphs Willem H. Haemers Digraphs and Matrices Jeffrey L. Stuart Bipartite Graphs and Matrices Bryan L. Shader Sign Pattern Matrices Frank J. Hall and Zhongshan Li Topics in Combinatorial Matrix Theory Permanents 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 Hogben Spectral Graph Theory Steve Butler and Fan Chung Algebraic Connectivity Steve Kirkland Matrix Completion Problems Luz M. DeAlba, Leslie Hogben, and Amy Wangsness Wehe Numerical Methods Numerical Methods for Linear Systems Vector and Matrix Norms, Error Analysis, Efficiency, and Stability Ralph Byers and Biswa Nath Datta Matrix Factorizations and Direct Solution of Linear Systems Christopher Beattie Least Squares Solution of Linear Systems Per Christian Hansen and Hans Bruun Nielsen Sparse Matrix Methods Esmond G. Ng Iterative Solution Methods for Linear Systems Anne Greenbaum Numerical Methods for Eigenvalues Symmetric Matrix Eigenvalue Techniques Ivan Slapnicar Unsymmetric Matrix Eigenvalue Techniques David S. Watkins The 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 Algebra Fast 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 Disciplines Applications to Physical and Biological Sciences Linear Algebra and Mathematical Physics Lorenzo Sadun Linear Algebra in Biomolecular Modeling Zhijun Wu Linear Algebra in Mathematical Population Biology and Epidemiology Fred Brauer and Carlos Castillo-Chavez Applications to Optimization Linear Programming Leonid N. Vaserstein Semidefinite Programming Henry Wolkowicz Applications to Probability and Statistics Random 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. Styan Markov Chains Beatrice Meini Applications to Computer Science Coding 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 Analysis Differential 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 Geometry Geometry Mark Hunacek Some Applications of Matrices and Graphs in Euclidean Geometry Miroslav Fiedler Applications to Algebra Matrix Groups Peter J. Cameron Group Representations Randall R. Holmes and Tin-Yau Tam Nonassociative Algebras Murray R. Bremner, Lucia I. Murakami, and Ivan P. Shestakov Lie Algebras Robert Wilson Computational Software Interactive Software for Linear Algebra MATLAB Steven J. Leon Linear 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 Algebra BLAS 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

About the Author :
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.

Review :
"The second edition is substantially expanded … A huge amount of thought has gone into the book. … Leslie Hogben has done an outstanding job to produce a book of this size in a uniform style with such a high standard of editing and typesetting. … this is certainly a book to ask your library to order and maybe even to purchase yourself." —Nick Higham (University of Manchester) on his blog http://nickhigham.wordpress.com, March 2014 Praise for the First Edition: "… a valuable compendium of information on virtually all aspects of linear algebra and its applications. …This is a Herculean labor of love on the editor’s part, a successful effort that should be appreciated and applauded by anyone working and/or teaching in this important area of mathematics. … Every library that supports mathematics and science departments should have this encyclopedic work on its shelves." —Henry Ricardo, MAA Reviews, June 2007 "Without doubts, it will be of great help for everybody who needs linear algebra in his profession, or for instructors or students looking for concepts, results, or examples." —H. Mitsch, Monatshefte fur Math, 2007 "This handbook covers all the major topics of linear algebra at both graduate and undergraduate level, as well as their applications and related software packages. The handbook will be without a doubt a valuable resource for anyone using linear algebra, i.e. basically for any mathematician." —EMS Newsletter