David C.Lay:是一位教育家,发表过30余篇关于函数分析和线性代数的研究论文。他还是由美国国家科学基金会资助的线性代数课程研究小组的创始人。Lay参与编写了包括“Introduction to Functional Analysis”、“Calculus and Its Applications”和“Linear Algebra Gems-A
目录:
CHAPTER 1 Linear Equations in Linear Algebra
INTRODUCTORY EXAMPLE:Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in business,Science,and Engineering
Supplementary Exercise
CHAPTER 2 Matrix Algebra
INTRODUCTORY EXAMPLE:Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input-Output Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank
Supplementary Exercise
CHAPTER 3 Determinants
INTRODUCTORY EXAMPLE:Determinants in Analytic Geometry
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule,Volume,and Linear Transformations
Supplementary Exercise
CHAPTER 4 Vector Spaces
INTRODUCTORY EXAMPLE:Space Flight and Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces,Column Spaces,and Linear Transformations
4.3 Linearly Independent Sets;Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercise
CHAPTER 5 Eigenvalues and Eigenvectors
INTRODUCTORY EXAMPLE:Dynamical Systems
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
Supplementary Exercise
CHAPTER 6 Orthogonality and Least Squares
INTRODUCTORY EXAMPLE:Readjusting the North American Datum