图书信息
图书目录
线性代数与矩阵：第二教程（影印版）
暂无简介
作者：
Helene Shapiro
定价：
135.00元
出版时间：
2022-02-28
ISBN：
978-7-04-057031-1
物料号：
57031-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数学
重点项目：
暂无
版面字数：
571.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Chapter 1. Preliminaries
- 1.1. Vector Spaces
- 1.2. Bases and Coordinates
- 1.3. Linear Transformations
- 1.4. Matrices
- 1.5. The Matrix of a Linear Transformation
- 1.6. Change of Basis and Similarity
- 1.7. Transposes
- 1.8. Special Types of Matrices
- 1.9. Submatrices, Partitioned Matrices, and Block Multiplication
- 1.10. Invariant Subspaces
- 1.11. Determinants
- 1.12. Tensor Products
- Exercises
- Chapter 2. Inner Product Spaces and Orthogonality
- 2.1. The Inner Product
- 2.2. Length, Orthogonality, and Projection onto a Line
- 2.3. Inner Products in Cn
- 2.4. Orthogonal Complements and Projection onto a Subspace
- 2.5. Hilbert Spaces and Fourier Series
- 2.6. Unitary Tranformations
- 2.7. The Gram–Schmidt Process and QR Factorization
- 2.8. Linear Functionals and the Dual Space
- Exercises
- Chapter 3. Eigenvalues, Eigenvectors, Diagonalization, and Triangularization
- 3.1. Eigenvalues
- 3.2. Algebraic and Geometric Multiplicity
- 3.3. Diagonalizability
- 3.4. A Triangularization Theorem
- 3.5. The Gerˇsgorin Circle Theorem
- 3.6. More about the Characteristic Polynomial
- 3.7. Eigenvalues of AB and BA
- Exercises
- Chapter 4. The Jordan and Weyr Canonical Forms
- 4.1. A Theorem of Sylvester and Reduction to Block Diagonal Form
- 4.2. Nilpotent Matrices
- 4.3. The Jordan Form of a General Matrix
- 4.4. The Cayley–Hamilton Theorem and the Minimal Polynomial
- 4.5. Weyr Normal Form
- Exercises
- Chapter 5. Unitary Similarity and Normal Matrices
- 5.1. Unitary Similarity
- 5.2. Normal Matrices—the Spectral Theorem
- 5.3. More about Normal Matrices
- 5.4. Conditions for Unitary Similarity
- Exercises
- Chapter 6. Hermitian Matrices
- 6.1. Conjugate Bilinear Forms
- 6.2. Properties of Hermitian Matrices and Inertia
- 6.3. The Rayleigh–Ritz Ratio and the Courant–Fischer Theorem
- 6.4. Cauchy’s Interlacing Theorem and Other Eigenvalue Inequalities
- 6.5. Positive Definite Matrices
- 6.6. Simultaneous Row and Column Operations
- 6.7. Hadamard’s Determinant Inequality
- 6.8. Polar Factorization and Singular Value Decomposition
- Exercises
- Chapter 7. Vector and Matrix Norms
- 7.1. Vector Norms
- 7.2. Matrix Norms
- Exercises
- Chapter 8. Some Matrix Factorizations
- 8.1. Singular Value Decomposition
- 8.2. Householder Transformations
- 8.3. Using Householder Transformations to Get Triangular, Hessenberg, and Tridiagonal Forms
- 8.4. Some Methods for Computing Eigenvalues
- 8.5. LDU Factorization
- Exercises
- Chapter 9. Field of Values
- 9.1. Basic Properties of the Field of Values
- 9.2. The Field of Values for Two-by-Two Matrices
- 9.3. Convexity of the Numerical Range
- Exercises
- Chapter 10. Simultaneous Triangularization
- 10.1. Invariant Subspaces and Block Triangularization
- 10.2. Simultaneous Triangularization, Property P, and Commutativity
- 10.3. Algebras, Ideals, and Nilpotent Ideals
- 10.4. McCoy’s Theorem
- 10.5. Property L
- Exercises
- Chapter 11. Circulant and Block Cycle Matrices
- 11.1. The J Matrix
- 11.2. Circulant Matrices
- 11.3. Block Cycle Matrices
- Exercises
- Chapter 12. Matrices of Zeros and Ones
- 12.1. Introduction: Adjacency Matrices and Incidence Matrices
- 12.2. Basic Facts about (0, 1)-Matrices
- 12.3. The Minimax Theorem of K¨onig and Egerv´ary
- 12.4. SDRs, a Theorem of P. Hall, and Permanents
- 12.5. Doubly Stochastic Matrices and Birkhoff’s Theorem
- 12.6. A Theorem of Ryser
- Exercises
- Chapter 13. Block Designs
- 13.1. t-Designs
- 13.2. Incidence Matrices for 2-Designs
- 13.3. Finite Projective Planes
- 13.4. Quadratic Forms and the Witt Cancellation Theorem
- 13.5. The Bruck–Ryser–Chowla Theorem
- Exercises
- Chapter 14. Hadamard Matrices
- 14.1. Introduction
- 14.2. The Quadratic Residue Matrix and Paley’s Theorem
- 14.3. Results of Williamson
- 14.4. Hadamard Matrices and Block Designs
- 14.5. A Determinant Inequality, Revisited
- Exercises
- Chapter 15. Graphs
- 15.1. Definitions
- 15.2. Graphs and Matrices
- 15.3. Walks and Cycles
- 15.4. Graphs and Eigenvalues
- 15.5. Strongly Regular Graphs
- Exercises
- Chapter 16. Directed Graphs
- 16.1. Definitions
- 16.2. Irreducibility and Strong Connectivity
- 16.3. Index of Imprimitivity
- 16.4. Primitive Graphs
- Exercises
- Chapter 17. Nonnegative Matrices
- 17.1. Introduction
- 17.2. Preliminaries
- 17.3. Proof of Perron’s Theorem
- 17.4. Nonnegative Matrices
- 17.5. Irreducible Matrices
- 17.6. Primitive and Imprimitive Matrices
- Exercises
- Chapter 18. Error-Correcting Codes
- 18.1. Introduction
- 18.2. The Hamming Code
- 18.3. Linear Codes: Parity Check and Generator Matrices
- 18.4. The Hamming Distance
- 18.5. Perfect Codes and the Generalized Hamming Code
- 18.6. Decoding
- 18.7. Codes and Designs
- 18.8. Hadamard Codes
- Exercises
- Chapter 19. Linear Dynamical Systems
- 19.1. Introduction
- 19.2. A Population Cohort Model
- 19.3. First-Order, Constant Coefficient, Linear Differential and Difference Equations
- 19.4. Constant Coefficient, Homogeneous Systems
- 19.5. Constant Coefficient, Nonhomogeneous Systems
- 19.6. Nonnegative Systems
- 19.7. Markov Chains
- Exercises
- Bibliography
- Index
