内容简介
《Linear Algebra》是由Stephen H. Friedberg、Arnold J. Insel和Lawrence E. Spence合著的一本经典线性代数教材，自首次出版以来，一直被广泛用于全球高校的线性代数课程。本书第四版于2003年出版，内容全面，深入浅出，适合本科生和研究生使用。
本书从向量空间的基本概念出发，系统介绍了线性代数的主要理论和方法。内容包括向量空间、线性变换、矩阵、行列式、特征值与特征向量、内积空间、对角化、若尔当标准型等。书中注重理论与应用的结合，提供了大量例题和习题，帮助读者深入理解线性代数的核心思想。
此外，本书还强调线性代数的几何直观和实际应用，如最小二乘法、线性微分方程等。其严谨的数学表述和丰富的练习使其成为学习线性代数的理想教材。
目录
Title
Copyright
Contents
Preface
Chapter 1 Vector Spaces
1.1 Introduction
Exercises
1.2 Vector Spaces
Exercises
1.3 Subspaces
Exercises
1.4 Linear Combinations and Systems of Linear Equations
Exercises
1.5 Linear Dependence and Linear Independence
Exercises
1.6 Bases and Dimension
Exercises
1.7* Maximal Linearly Independent Subsets
Chapter 2 Linear Transformations and Matrices
2.1 Linear Transformations, Null Spaces, and Ranges
Copyright
Contents
Preface
Chapter 1 Vector Spaces
1.1 Introduction
Exercises
1.2 Vector Spaces
Exercises
1.3 Subspaces
Exercises
1.4 Linear Combinations and Systems of Linear Equations
Exercises
1.5 Linear Dependence and Linear Independence
Exercises
1.6 Bases and Dimension
Exercises
1.7* Maximal Linearly Independent Subsets
Chapter 2 Linear Transformations and Matrices
2.1 Linear Transformations, Null Spaces, and Ranges
Exercises
2.2 The Matrix Representation of a Linear Transformation
Exercises
2.3 Composition of Linear Transformations and Matrix Multiplication
Exercises
2.4 Invertibility and Isomorphisms
Exercises
2.5 The Change of Coordinate Matrix
Exercises
2.6* Dual Spaces
Exercises
2.7* Homogeneous Linear Differential Equations with Constant Coefficients
Chapter 3 Elementary Matrix Operations and Systems of Linear Equations
3.1 Elementary Matrix Operations and Elementary Matrices
Exercises
3.2 The Rank of a Matrix and Matrix Inverses
Exercises
3.3 Systems of Linear Equations—Theoretical Aspects
Exercises
3.4 Systems of Linear Equations—Computational Aspects
Chapter 4 Determinants
4.1 Determinants of Order 2
Exercises
4.2 Determinants of Order n
Exercises
4.3 Properties of Determinants
Exercises
4.4 Summary——Important Facts about Determinants
Exercises
4.5* A Characterization of the Determinant
Chapter 5 Diagonalization
5.1 Eigenvalues and Eigenvectors
Exercises
5.2 Diagonalizability
Exercises
5.3* Matrix Limits and Markov Chains
Exercises
5.4 Invariant Subspaces and the Cayley–Hamilton Theorem
Chapter 6 Inner Product Spaces
6.1 Inner Products and Norms
Exercises
6.2 The Gram–Schmidt Orthogonalization Process and Orthogonal Complements
Exercises
6.3 The Adjoint of a Linear Operator
Exercises
6.4 Normal and Self-Adjoint Operators
Exercises
6.5 Unitary and Orthogonal Operators and Their Matrices
Exercises
6.6 Orthogonal Projections and the Spectral Theorem
Exercises
6.7* The Singular Value Decomposition and the Pseudoinverse
Exercises
6.8* Bilinear and Quadratic Forms
Exercises
6.9* Einstein’s Special Theory of Relativity
Exercises
6.10* Conditioning and the Rayleigh Quotient
Exercises
6.11* The Geometry of Orthogonal Operators
Chapter 7 Canonical Forms
7.1 The Jordan Canonical Form I
Exercises
7.2 The Jordan Canonical Form II
Exercises
7.3 The Minimal Polynomial
Exercises
7.4* The Rational Canonical Form
Appendices
A Sets
B Functions
C Fields
D Complex Numbers
E Polynomials
Answers to Selected Exercises
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
2.2 The Matrix Representation of a Linear Transformation
Exercises
2.3 Composition of Linear Transformations and Matrix Multiplication
Exercises
2.4 Invertibility and Isomorphisms
Exercises
2.5 The Change of Coordinate Matrix
Exercises
2.6* Dual Spaces
Exercises
2.7* Homogeneous Linear Differential Equations with Constant Coefficients
Chapter 3 Elementary Matrix Operations and Systems of Linear Equations
3.1 Elementary Matrix Operations and Elementary Matrices
Exercises
3.2 The Rank of a Matrix and Matrix Inverses
Exercises
3.3 Systems of Linear Equations—Theoretical Aspects
Exercises
3.4 Systems of Linear Equations—Computational Aspects
Chapter 4 Determinants
4.1 Determinants of Order 2
Exercises
4.2 Determinants of Order n
Exercises
4.3 Properties of Determinants
Exercises
4.4 Summary——Important Facts about Determinants
Exercises
4.5* A Characterization of the Determinant
Chapter 5 Diagonalization
5.1 Eigenvalues and Eigenvectors
Exercises
5.2 Diagonalizability
Exercises
5.3* Matrix Limits and Markov Chains
Exercises
5.4 Invariant Subspaces and the Cayley–Hamilton Theorem
Chapter 6 Inner Product Spaces
6.1 Inner Products and Norms
Exercises
6.2 The Gram–Schmidt Orthogonalization Process and Orthogonal Complements
Exercises
6.3 The Adjoint of a Linear Operator
Exercises
6.4 Normal and Self-Adjoint Operators
Exercises
6.5 Unitary and Orthogonal Operators and Their Matrices
Exercises
6.6 Orthogonal Projections and the Spectral Theorem
Exercises
6.7* The Singular Value Decomposition and the Pseudoinverse
Exercises
6.8* Bilinear and Quadratic Forms
Exercises
6.9* Einstein’s Special Theory of Relativity
Exercises
6.10* Conditioning and the Rayleigh Quotient
Exercises
6.11* The Geometry of Orthogonal Operators
Chapter 7 Canonical Forms
7.1 The Jordan Canonical Form I
Exercises
7.2 The Jordan Canonical Form II
Exercises
7.3 The Minimal Polynomial
Exercises
7.4* The Rational Canonical Form
Appendices
A Sets
B Functions
C Fields
D Complex Numbers
E Polynomials
Answers to Selected Exercises
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
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本书由书友@214ouo发布分享，仅供学习交流使用，版权归原作者所有。如有侵权，请联系我们删除。
本书由书友@214ouo发布分享，仅供学习交流使用，版权归原作者所有。如有侵权，请联系我们删除。
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