线性代数（英文版·第7版）

PREFACE.  
1  MATRICES AND SYSTEMS OF EQUATIONS  
1 Systems of Linear Equations  
2 Row Echelon Form  
3 Matrix Algebra  
4 Elementary Matrices  
5 Partitioned Matrices  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
2 DETERMINANTS  
1 The Determinant of a Matrix  
2 Properties of Determinants  
3 Cramer's Rule  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
3 VECTOR SPACES  
1 Definition and Examples  
2 Subspaces  
3 Linear Independence  
4 Basis and Dimension  
5 Change of Basis  
6 Row Space and Column Space  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
4 LINEAR TRANSFORMATIONS  
1 Definition and Examples  
2 Matrix Representations of Linear Transformations  
3 Similarity  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
5 ORTHOGONALITY  
1 The Scalar Product in Rn  
2 Orthogonal Subspaces  
3 Least Squares Problems  
4 Inner Product Spaces  
5 Orthonormal Sets  
6 The Gram-Schmidt Orthogonalization Process  
7 Orthogonal Polynomials  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
6 EIGENVALUES  
1 Eigenvalues and Eigenvectors  
2 Systems of Linear Differential Equations  
3 Diagonalization  
4 Hermitian Matrices  
5 The Singular Value Decomposition  
G Quadrati Forms  
7 Positive Definite Matrices  
8 Nonnegative Matrices  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
7 NUMERICAL LINEAR ALGEBRA  
1 Floating-Point Numbers  
2 Gaussian Elimination  
3 Pivoting Strategies  
4 Matrix Norms and Condition Numbers  
5 Orthogonal Transformations  
6 The Eigenvalue Problem  
7 Least Squares Problems  
MATLAB Exercises  
Chapter Test A  
Chapter Test B  
8 ITERATIVE METHODS  
9 CANONICAL FORMS  
APPENDIX: MATLAB  
BIBLIOGRAPHY  
ANSWERS TO SELECTED EXERCISES  
INDEX