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Book

Handbook of Linear Algebra

Book

Handbook of Linear Algebra

DOI link for Handbook of Linear Algebra

Handbook of Linear Algebra book

Handbook of Linear Algebra

DOI link for Handbook of Linear Algebra

Handbook of Linear Algebra book

Edited ByLeslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias
Edition 1st Edition
First Published 2006
eBook Published 2 November 2006
Pub. Location Boca Raton
Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781420010572
Pages 1400
eBook ISBN 9780429138492
Subjects Engineering & Technology, Mathematics & Statistics
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Hogben, L., Brualdi, R., Greenbaum, A., & Mathias, R. (Eds.). (2006). Handbook of Linear Algebra (1st ed.). CRC Press. https://doi.org/10.1201/9781420010572

ABSTRACT

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 accessibl

TABLE OF CONTENTS

part I

Linear Algebra

section

Basic Linear Algebra

chapter 1

Vectors, Matrices, and Systems of Linear Equations

ByJane Day

chapter 2

Linear Independence, Span, and Bases

ByMark Mills

chapter 3

Linear Transformations

ByFrancesco Barioli

chapter 4

Determinants and Eigenvalues

ByLuz M. DeAlba

chapter 5

Inner Product Spaces, Orthogonal Projection, Least Squares

ByLixing Han, Michael Neumann

section

Matrices with Special Properties

chapter 6

Canonical Forms

ByLeslie Hogben

chapter 7

Unitary Similarity, Normal Matrices, and Spectral Theory

ByHelene Shapiro

chapter 8

Hermitian and Positive Definite Matrices

ByWayne Barrett

chapter 9

Nonnegative Matrices and Stochastic Matrices

ByUriel G. Rothblum

chapter 10

Partitioned Matrices

ByRobert Reams

section

Advanced Linear Algebra

chapter 11

Functions of Matrices

ByNicholas J. Higham

chapter 12

Quadratic, Bilinear, and Sesquilinear Forms

ByRaphael Loewy

chapter 13

Multilinear Algebra

ByJosé A. Dias da Silva, Armando Machado

chapter 14

Matrix Equalities and Inequalities

ByMichael Tsatsomeros

chapter 15

Matrix Perturbation Theory

ByRen-Cang Li

chapter 16

Pseudospectra

ByMark Embree

chapter 17

Singular Values and Singular Value Inequalities

ByRoy Mathias

chapter 18

Numerical Range

ByChi-Kwong Li

chapter 19

Matrix Stability and Inertia

ByDaniel Hershkowitz

section

Topics in Advanced Linear Algebra

chapter 20

Inverse Eigenvalue Problems

ByAlberto Borobia

chapter 21

Totally Positive and Totally Nonnegative Matrices

ByShaun M. Fallat

chapter 22

Linear Preserver Problems

ByPeter Šemrl

chapter 23

Matrices over Integral Domains

ByShmuel Friedland

chapter 24

Similarity of Families of Matrices

ByShmuel Friedland

chapter 25

Max-Plus Algebra

ByMarianne Akian, Ravindra Bapat, Stéphane Gaubert

chapter 26

Matrices Leaving a Cone Invariant

ByBit-Shun Tam, Hans Schneider

part II

Combinatorial Matrix Theory and Graphs

section

Matrices and Graphs

chapter 27

Combinatorial Matrix Theory

ByRichard A. Brualdi

chapter 28

Matrices and Graphs

ByWillem H. Haemers

chapter 29

Digraphs and Matrices

ByJeffrey L. Stuart

chapter 30

Bipartite Graphs and Matrices

ByBryan L. Shader

section

Topics in Combinatorial Matrix Theory

chapter 31

Permanents

ByIan M. Wanless

chapter 32

D-Optimal Matrices

ByMichael G. Neubauer, William Watkins

chapter 33

Sign Pattern Matrices

ByFrank J. Hall, Zhongshan Li

chapter 34

Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph

ByCharles R. Johnson, António Leal Duarte, Carlos M. Saiago

chapter 35

Matrix Completion Problems

ByLeslie Hogben, Amy Wangsness

chapter 36

Algebraic Connectivity

BySteve Kirkland

part III

Numerical Methods

section

Numerical Methods for Linear Systems

chapter 37

Vector and Matrix Norms, Error Analysis, Efficiency, and Stability

ByRalph Byers, Biswa Nath Datta

chapter 38

Matrix Factorizations and Direct Solution of Linear Systems

ByChristopher Beattie

chapter 39

Least Squares Solution of Linear Systems

ByPer Christian Hansen, Hans Bruun Nielsen

chapter 40

Sparse Matrix Methods

ByEsmond G. Ng

chapter 41

Iterative Solution Methods for Linear Systems

ByAnne Greenbaum

section

Numerical Methods for Eigenvalues

chapter 42

Symmetric Matrix Eigenvalue Techniques

ByIvan Slapničar

chapter 43

Unsymmetric Matrix Eigenvalue Techniques

ByDavid S. Watkins

chapter 44

The Implicitly Restarted Arnoldi

ByD.C. Sorensen

chapter 45

Computation of the Singular Value Decomposition

ByAlan Kaylor Cline, Inderjit S. Dhillon

chapter 46

Computing Eigenvalues and Singular Values to High Relative Accuracy

ByZlatko Drmač

section

Computational Linear Algebra

chapter 47

Fast Matrix Multiplication

ByDario A. Bini

chapter 48

Structured Matrix Computations

ByMichael Ng

chapter 49

Large-Scale Matrix Computations

ByRoland W. Freund

part IV

Applications

section

Applications to Optimization

chapter 50

Linear Programming

ByLeonid N. Vaserstein

chapter 51

Semidefinite Programming

ByHenry Wolkowicz

section

Applications to Probability and Statistics

chapter 52

Random Vectors and Linear Statistical Models

BySimo Puntanen, George P.H. Styan

chapter 53

Multivariate Statistical Analysis

BySimo Puntanen, George A.F. Seber, George P.H. Styan

chapter 54

Markov Chains

ByBeatrice Meini

section

Applications to Analysis

chapter 55

Differential Equations and Stability

ByVolker Mehrmann, Tatjana Stykel

chapter 56

Dynamical Systems and Linear Algebra

ByFritz Colonius, Wolfgang Kliemann

chapter 57

Control Theory

ByPeter Benner

chapter 58

Fourier Analysis

ByKenneth Howell

section

Applications to Physical and Biological Sciences

chapter 59

Linear Algebra and Mathematical Physics

ByLorenzo Sadun

chapter 60

Linear Algebra in Biomolecular Modeling

ByZhijun Wu

section

Applications to Computer Science

chapter 61

Coding Theory

ByJoachim Rosenthal, Paul Weiner

chapter 62

Quantum Computation

ByZijian Diao

chapter 63

Information Retrieval and Web Search

ByAmy N. Langville, Carl D. Meyer

chapter 64

Signal Processing

ByMichael Stewart

section

Applications to Geometry

chapter 65

Geometry

ByMark Hunacek

chapter 66

Some Applications of Matrices and Graphs in Euclidean Geometry

ByMiroslav Fiedler

section

Applications to Algebra

chapter 67

Matrix Groups

ByPeter J. Cameron

chapter 68

Group Representations

ByRandall R. Holmes, T.Y. Tam

chapter 69

Nonassociative Algebras

ByMurray R. Bremner, Lucia I. Murakami, Ivan P. Shestakov

chapter 70

Lie Algebras

ByRobert Wilson

part V

Computational Software

section

Interactive Software for Linear Algebra

chapter 71

Matlab®

BySteven J. Leon

chapter 72

Linear Algebra in Maple®

ByDavid J. Jeffrey, Robert M. Corless

chapter 73

Mathematica

ByHeikki Ruskeepää

section

Packages of Subroutines for Linear Algebra

chapter 74

BLAS

ByJack Dongarra, Victor Eijkhout, Julien Langou

chapter 75

Lapack

ByZhaojun Bai, James Demmel, Jack Dongarra, Julien Langou, Jenny Wang

chapter 76

Use of ARPACK and EIGS

ByD. C. Sorensen

chapter 77

Summary of Software for Linear Algebra Freely Available on the Web

ByJack Dongarra, Victor Eijkhout, Julien Langou
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