PREFACE
1 MATRICES AND SYSTEMS OF EQUATIONS
　1 Systems of Linear Equations
　2 Row Echelon Form
　3 Matrix Algebra
　4 Elementary Matrices
　S 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 Iinear 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 ORTHOGONALIT
　1 The Scalar Product in Rn
　2 Orthogonal Subspaces
　3 Least Squares Problems
　4 Inner Product Spaces
　5 Orthonormal Sets
　6 The GramSchmidt 0rthogonalization 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
　6 Quadratic Forms
　7 Positive Definite Matrices
　8 Nonnegative Matrices
　　MATLAB Exercises
　　Chapter Test A
　　Chapter Test B
7 NUMERICAL LINEAR ALGEBRA
　1 FloatingPoint 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