Handbook of Linear Algebra: (Discrete Mathematics and Its Applications)

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.

Table of Contents:
LINEAR ALGEBRA BASIC LINEAR ALGEBRA Vectors, Matrices and Systems of Linear Equations Linear Independence, Span, and Bases Linear Transformations Determinants and Eigenvalues Inner Product Spaces, Orthogonal Projection, Least Squares and Singular Value Decomposition MATRICES WITH SPECIAL PROPERTIES Canonical Forms Unitary Similarity, Normal Matrices and Spectral Theory Hermitian and Positive Definite Matrices Nonnegative and Stochastic Matrices Partitioned Matrices ADVANCED LINEAR ALGEBRA Functions of Matrices Quadratic, Bilinear and Sesquilinear Forms Multilinear Algebra Matrix Equalities and Inequalities Matrix Perturbation Theory Pseudospectra Singular Values and Singular Value Inequalities Numerical Range Matrix Stability and Inertia TOPICS IN ADVANCED LINEAR ALGEBRA Inverse Eigenvalue Problems Totally Positive and Totally Nonnegative Matrices Linear Preserver Problems Matrices over Integral Domains Similarity of Families of Matrices Max-Plus Algebra Matrices Leaving a Cone Invariant COMBINATORIAL MATRIX THEORY AND GRAPHS MATRICES AND GRAPHS Combinatorial Matrix Theory Matrices and Graphs Digraphs and Matrices Bipartite Graphs and Matrices TOPICS IN COMBINATORIAL MATRIX THEORY Permanents D-Optimal Designs Sign Pattern Matrices Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph Matrix Completion Problems Algebraic Connectivity NUMERICAL METHODS NUMERICAL METHODS FOR LINEAR SYSTEMS Vector and Matrix Norms, Error Analysis, Efficiency and Stability Matrix Factorizations and Direct Solution of Linear Systems Least Squares Solution of Linear Systems Sparse Matrix Methods Iterative Solution Methods for Linear Systems NUMERICAL METHODS FOR EIGENVALUES Symmetric Matrix Eigenvalue Techniques Unsymmetric Matrix Eigenvalue Techniques The Implicitly Restarted Arnoldi Method Computation of the Singular Value Decomposition Computing Eigenvalues and Singular Values to High Relative Accuracy COMPUTATIONAL LINEAR ALGEBRA Fast Matrix Multiplication Structured Matrix Computations Large-Scale Matrix Computations APPLICATIONS APPLICATIONS TO OPTIMIZATION Linear Programming Semidefinite Programming APPLICATIONS TO PROBABILITY AND STATISTICS Random Vectors and Linear Statistical Models Multivariate Statistical Analysis Markov Chains APPLICATIONS TO ANALYSIS Differential Equations and Stability Dynamical Systems and Linear Algebra Control Theory Fourier Analysis APPLICATIONS TO PHYSICAL AND BIOLOGICAL SCIENCES Linear Algebra and Mathematical Physics Linear Algebra in Biomolecular Modeling APPLICATIONS TO COMPUTER SCIENCE Coding Theory Quantum Computation Information Retrieval and Web Search Signal Processing APPLICATIONS TO GEOMETRY Geometry Some Applications of Matrices and Graphs in Euclidean Geometry APPLICATIONS TO ALGEBRA Matrix Groups Group Representations Nonassociative Algebras Lie Algebras COMPUTATIONAL SOFTWARE INTERACTIVE SOFTWARE FOR LINEAR ALGEBRA MATLAB Linear Algebra in Maple Mathematica PACKAGES OF SUBROUTINES FOR LINEAR ALGEBRA BLAS LAPACK Use of ARPACK and EIGS Summary of Software for Linear Algebra Freely Available on the Web GLOSSARY NOTATION INDEX INDEX