# Handbook of Linear Algebra

## Book Description

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

Part I. Linear Algebra

Chapter 1. Vectors, Matrices, and Systems of Linear Equations

Chapter 2. Linear Independence, Span, and Bases

Chapter 3. Linear Transformations

Chapter 4. Determinants and Eigenvalues

Chapter 5. Inner Product Spaces, Orthogonal Projection, Least Squares, and Singular Value Decomposition

Chapter 6. Canonical Forms

Chapter 7. Unitary Similarity, Normal Matrices, and Spectral Theory

Chapter 8. Hermitian and Positive Definite Matrices

Chapter 9. Nonnegative Matrices and Stochastic Matrices

Chapter 10. Partitioned Matrices

Chapter 11. Functions of Matrices

Chapter 12. Quadratic, Bilinear, and Sesquilinear Forms

Chapter 13. Multilinear Algebra

Chapter 14. Matrix Equalities and Inequalities

Chapter 15. Matrix Perturbation Theory

Chapter 16. Pseudospectra

Chapter 17. Singular Values and Singular Value Inequalities

Chapter 18. Numerical Range

Chapter 19. Matrix Stability and Inertia

Chapter 20. Inverse Eigenvalue Problems

Chapter 21. Totally Positive and Totally Nonnegative Matrices

Chapter 22. Linear Preserver Problems

Chapter 23. Matrices over Integral Domains

Chapter 24. Similarity of Families of Matrices

Chapter 25. Max-Plus Algebra

Chapter 26. Matrices Leaving a Cone Invariant

Part II. Combinatorial Matrix Theory and Graphs

Chapter 27. Combinatorial Matrix Theory

Chapter 28. Matrices and Graphs

Chapter 29. Digraphs and Matrices

Chapter 30. Bipartite Graphs and Matrices

Chapter 31. Permanents

Chapter 32. D-Optimal Matrices

Chapter 33. Sign Pattern Matrices

Chapter 34. Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph

Chapter 35. Matrix Completion Problems

Chapter 36. Algebraic Connectivity

Part III. Numerical Methods

Chapter 37. Vector and Matrix Norms, Error Analysis, Efficiency, and Stability

Chapter 38. Matrix Factorizations and Direct Solution of Linear Systems

Chapter 39. Least Squares Solution of Linear Systems

Chapter 40. Sparse Matrix Methods

Chapter 41. Iterative Solution Methods for Linear Systems

Chapter 42. Symmetric Matrix Eigenvalue Techniques

Chapter 43. Unsymmetric Matrix Eigenvalue Techniques

Chapter 44. The Implicitly Restarted Arnoldi Methods

Chapter 45. Computation of the Singular Value Decomposition

Chapter 46. Computing Eigenvalues and Singular Values to High Relative Accuracy

Chapter 47. Fast Matrix Multiplication

Chapter 48. Structured Matrix Computations

Chapter 49. Large-Scale Matrix Computations

Part IV. Applications

Chapter 50. Linear Programming

Chapter 51. Semidefinite Programming

Chapter 52. Random Vectors and Linear Statistical Models

Chapter 53. Multivariate Statistical Analysis

Chapter 54. Markov Chains

Chapter 55. Differential Equations and Stability

Chapter 56. Dynamical Systems and Linear Algebra

Chapter 57. Control Theory

Chapter 58. Fourier Analysis

Chapter 59. Linear Algebra and Mathematical Physics

Chapter 60. Linear Algebra in Biomolecular Modeling

Chapter 61. Coding Theory

Chapter 62. Quantum Computation

Chapter 63. Information Retrieval and Web Search

Chapter 64. Signal Processing

Chapter 65. Geometry

Chapter 66. Some Applications of Matrices and Graphs in Euclidean Geometry

Chapter 67. Matrix Groups

Chapter 68. Group Representations

Chapter 69. Nonassociative Algebras

Chapter 70. Lie Algebras

Part V. Computational Software

Chapter 71. Matlab

Chapter 72. Linear Algebra in Maple

Chapter 73. Mathematica

Chapter 74. BLAS

Chapter 75. LAPACK

Chapter 76. Use of ARPACK and EIGS

Chapter 77. Summary of Software for Linear Algebra Freely Available on the Web

## Book Details

- Title: Handbook of Linear Algebra
- Author: Leslie Hogben
- Length: 1400 pages
- Edition: 1
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2006-11-02
- ISBN-10: 1584885106
- ISBN-13: 9781584885108

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