Chapter 1 Linear Equations in Linear Algebra001
1.1Systems of Linear Equations001
1.2Row Reduction and Echelon Forms008
1.3Solutions of Linear Systems012
1.4Vector Equations014
Exercises017

Chapter 2 Matrix Algebra019
2.1Matrix Operations019
2.2The Inverse of a Matrix024
2.3Partitoned Matrices028
2.4Matrix Factorizations031
2.5Subspace of Rn032
2.6Dimension and Rank035
Exercises037

Chapter 3 Determinants040
3.1Introduction to Determinants040
3.2Properties of Determinants043
3.3Cofactor Expansion048
3.4The Inverse of a Matrix050
3.5Cramer’s Rule053
Exercises054

Chapter 4 Vector Spaces058
4.1Definition of Vector Spaces058
4.2Subspaces and Span062
4.3Linearly Independent Sets068
4.4Bases and Dimension071
4.5Inner Product，Length，Angle074
4.6Orthonormal Basis and the Gram-Schmidt Procedure078
Exercises084

Chapter 5 Eigenvalues and Eigenvectors088
5.1Definition of Eigenvalues and Eigenvectors088
5.2Properties of Eigenvalues and Eigenvectors092
5.3Similarity and Diagonalization096
5.4Diagonalization of Symmetric Matrices100
Exercises105

Chapter 6 Solution Sets of Linear Systems107
6.1Homogeneous Linear Systems107
6.2Solutions of Nonhomogeneous Systems108
6.3Applications of Linear Systems110
Exercises113

Chapter 7 Symmetric Matrices and Quadratic Forms117
7.1Diagonalization of Symmetric Matrices117
7.2Quadratic Forms119
7.3Quadratic Problems122
7.4The Singular Value Decomposition126
7.5Applications to Statistics129
Exercises132

References134