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C5106 FL

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Editor-in-Chief Leslie Hogben, Iowa State University, Ames, USA Associate Editors Richard A. Brualdi, University of Wisconsin–Madison, USA Anne Greenbaum, University of Washington, Seattle, USA Roy Mathias, University of Birmingham, UK

A volume in the series Discrete and Its Applications Edited by Kenneth H. Rosen, Monmouth University, West Long Branch, New Jersey, USA Contents

LINEAR ALGEBRA A COMPLETE TREATMENT OF BASIC LINEAR ALGEBRA The Handbook of Linear Algebra provides comprehensive cover- Vectors, Matrices and Systems of Linear age of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The , Span, and Bases esteemed international contributors guide you from the very ele- Linear Transformations mentary aspects of the subject to the frontiers of current research. and Eigenvalues The book features an accessible layout of parts, chapters, and sec- Inner Product Spaces, Orthogonal tions, with each section containing definition, fact, and example Projection, Least Squares and Singular segments. The five main parts of the book encompass the funda- Value Decomposition mentals of linear algebra, combinatorial and numerical linear alge- bra, applications of linear algebra to various mathematical and non- MATRICES WITH SPECIAL PROPERTIES mathematical disciplines, and software packages for linear algebra Canonical Forms computations. Within each section, the facts (or theorems) are pre- Unitary Similarity, Normal Matrices and sented in a list format and include references for each fact to encourage further reading, Spectral Theory while the examples illustrate both the definitions and the facts. Hermitian and Positive Definite Matrices Linearization often enables difficult problems to be estimated by more manageable linear Nonnegative and Stochastic Matrices ones, making the Handbook of Linear Algebra essential reading for professionals who Partitioned Matrices deal with an assortment of mathematical problems. ADVANCED LINEAR ALGEBRA Functions of Matrices Features Quadratic, Bilinear and Sesquilinear Forms • Presents basic as well as advanced linear algebra concepts, such as Matrix Equalities and Inequalities and inverse eigenvalue problems Matrix Perturbation Theory • Features matrix notation throughout the text Pseudospectra Singular Values and • Covers combinatorial and numerical linear algebra—two important branches Inequalities of linear algebra Numerical Range • Explores both mathematical and nonmathematical applications, such as quantum Matrix Stability and Inertia computing, , , and computational biology TOPICS IN ADVANCED LINEAR • Discusses software packages useful for linear algebra computations, including ALGEBRA MATLAB®, ™, and Mathematica® Inverse Eigenvalue Problems Totally Positive and Totally Nonnegative • Provides numerous references for additional information along with a glossary that Matrices covers all major linear algebra terminology Linear Preserver Problems Matrices over Integral Domains Similarity of Families of Matrices Max-Plus Algebra Matrices Leaving a Cone Invariant COMBINATORIAL MATRIX THEORY Catalog no. C5106, January 2007, 1400 pp. AND GRAPHS ISBN: 978-1-58488-510-8, $119.95 / £68.99 MATRICES AND GRAPHS Combinatorial Matrix Theory Matrices and Graphs ORDER ONLINE AT Digraphs and Matrices Bipartite Graphs and Matrices See reverse for continuation of contents and ordering information C5106 FL.qxd 3/14/07 5:07 PM Page 2

Contents continued – Handbook of Linear Algebra TOPICS IN COMBINATORIAL MATRIX COMPUTATIONAL LINEAR ALGEBRA APPLICATIONS TO GEOMETRY THEORY Fast Geometry Permanents Structured Matrix Computations Some Applications of Matrices and Graphs in D-Optimal Designs Large-Scale Matrix Computations Euclidean Geometry Sign Pattern Matrices APPLICATIONS APPLICATIONS TO ALGEBRA Multiplicity Lists for the Eigenvalues of APPLICATIONS TO OPTIMIZATION Matrix Groups Symmetric Matrices with a Given Graph Group Representations Matrix Completion Problems Linear Programming Semidefinite Programming Nonassociative Algebras Algebraic Connectivity Lie Algebras NUMERICAL METHODS APPLICATIONS TO PROBABILITY AND STA- TISTICS COMPUTATIONAL SOFTWARE NUMERICAL METHODS FOR LINEAR Random Vectors and Linear Statistical Models INTERACTIVE SOFTWARE FOR LINEAR SYSTEMS Multivariate Statistical Analysis ALGEBRA Vector and Matrix Norms, Error Analysis, MATLAB Efficiency and Stability Markov Chains Linear Algebra in Maple Matrix Factorizations and Direct Solution of APPLICATIONS TO ANALYSIS Linear Systems Differential Equations and Stability Mathematica Least Squares Solution of Linear Systems Dynamical Systems and Linear Algebra PACKAGES OF SUBROUTINES FOR LINEAR Methods Control Theory ALGEBRA Iterative Solution Methods for Linear Systems BLAS LAPACK NUMERICAL METHODS FOR EIGENVALUES APPLICATIONS TO PHYSICAL AND Use of ARPACK and EIGS Symmetric Matrix Eigenvalue Techniques BIOLOGICAL SCIENCES Linear Algebra and Summary of Software for Linear Algebra Freely Unsymmetric Matrix Eigenvalue Techniques Available on the Web The Implicitly Restarted Arnoldi Method Linear Algebra in Biomolecular Modeling Computation of the Singular Value APPLICATIONS TO SCIENCE GLOSSARY Decomposition NOTATION INDEX Computing Eigenvalues and Singular Values to Quantum Computation High Relative Accuracy INDEX Information Retrieval and Web Search Signal Processing

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