• 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: True or False
• Chapter Test B

• 2.1 The Determinant of a Matrix
• 2.2 Properties of Determinants
• 2.3 Additional Topics and Applications
• MATLAB Exercises
• Chapter Test A: True or False
• Chapter Test B

• 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: True or False
• Chapter Test B

• 4.1 Definition and Examples
• 4.2 Matrix Representations of Linear Transformations
• 4.3 Similarity
• MATLAB Exercises
• Chapter Test A: True or False
• Chapter Test B

• 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: True or False
• Chapter Test B

• 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: True or False
• Chapter Test B

• 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
• 7.8 Iterative Methods
• MATLAB Exercises
• Chapter Test A: True or False
• Chapter Test B

• 8.1 Nilpotent Operators
• 8.2 The Jordan Canonical Form

Appendix: MATLAB

Bibliography

Answers to Selected Exercises

Index