Linear algebra with applications

　　
　　 Preface
　　1 Matrices and Systems of Equations
　　 1.1 Systems of Linear Equations
　　 1.2 Row Echelon Form
　　 1.3 Matrix Arithmetic
　　 1.4 Matrix Algebra
　　 1.5 Elementary Matrices
　　 1.6 Partitioned Matrices
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　2 Determinants
　　 2.1 The Detemainant of, a Matrix
　　 2.2 Properties of Determinants
　　 2.3 Additional Topics and Applications
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　3 Vector Spaces
　　 3.1 Definition and Examples
　　 3.2 Subspaces
　　 3.3 Linear Independence
　　 3.4 Basis and Dimension
　　 3.5 Change of Basis
　　 3.6 Row Space and Column Space
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　4 Linear Transformations
　　 4.1 Definition and Examples
　　 4.2 Matrix Representations of Linear Transformations
　　 4.3 Similarity
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　5 Orthogonality
　　 5.1 The Scalar Product in Rn
　　 5.2 Orthogonal Subspaces
　　 5.3 Least Squares Problems
　　 5.4 Inner Product Spaces
　　 5.5 Orthonormal Sets
　　 5.6 The Gram-Schmidt Orthogonalization Process
　　 5.7 Orthogonal Polynomials
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　6 Eigenvalues
　　 6.1 Eigenvalues and Eigenvectors
　　 6.2 Systems of Linear Differential Equations
　　 6.3 Diagonalization
　　 6.4 Hermitian Matrices
　　 6.5 The Singular Value Decomposition
　　 6.6 Quadratic Forms
　　 6.7 Positive Definite Matrices
　　 6.8 Nonnegative Matrices
　　 MATLAB Exercises
　　 Chapter Test A
　　 Chapter Test B
　　7 Numerical Linear Algebra
　　 7.1 Floating-Point Numbers
　　 7.2 Gaussian Elimination
　　 7.3 Pivoting Strategies
　　 7.4 Matrix Norms and Condition Numbers
　　 7.5 Orthogonal Transformations
　　 7.6 The Eigenvalue Problem
　　 7.7 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