Handbook of Linear Algebra (Hardcover)

Leslie Hogben

  • 出版商: Chapman
  • 出版日期: 2006-11-02
  • 售價: $1,850
  • 貴賓價: 9.8$1,813
  • 語言: 英文
  • 頁數: 1400
  • 裝訂: Hardcover
  • ISBN: 1584885106
  • ISBN-13: 9781584885108
  • 相關分類: 線性代數 Linear-algebra
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商品描述

Description 

  • Presents basic as well as advanced linear algebra concepts, such as matrix perturbation theory and inverse eigenvalue problems
  • Features matrix notation throughout the text
  • Covers combinatorial and numerical linear algebra-two important branches of linear algebra
  • Explores both mathematical and nonmathematical applications, such as quantum computing, control theory, signal processing, and computational biology
  • Discusses software packages useful for linear algebra computations, including MATLAB? Maple? and Mathematica?
  • Provides numerous references for additional information along with a glossary that covers all major linear algebra terminology

    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

商品描述(中文翻譯)

《線性代數手冊》提供了線性代數概念、應用和計算軟體包的全面涵蓋,以易於使用的手冊格式呈現。享有盛譽的國際貢獻者將引導您從該主題的基本方面到當前研究的前沿。

該書以部分、章節和節的易於理解的佈局呈現,每個節包含定義、事實和示例段落。該書的五個主要部分涵蓋了線性代數的基礎知識、組合和數值線性代數、線性代數在各種數學和非數學學科中的應用,以及用於線性代數計算的軟體包。在每個節中,事實(或定理)以列表格式呈現,並包含每個事實的參考資料以鼓勵進一步閱讀,而示例則既說明了定義又說明了事實。

線性化通常使得複雜的問題可以通過更易處理的線性問題來估計,這使得《線性代數手冊》成為處理各種數學問題的專業人士必讀的書籍。

《線性代數手冊》的目錄如下:

- 描述
- 基本線性代數概念
- 矩陣擾動理論和逆特徵值問題
- 矩陣表示法
- 組合和數值線性代數
- 線性代數在數學和非數學學科中的應用
- 線性代數計算的軟體包
- 附錄:線性代數術語詞彙表

請注意,本書的翻譯僅供參考,具體內容以原書為準。