## Table of Contents

Preface

What’s New in the Eighth Edition?

Computer Exercises

Overview of Text

Suggested Course Outlines

Supplementary Materials

Acknowledgments

**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 Determinant 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 *R*^{n}

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

Appendix: MATLAB

The MATLAB Desktop Display

Basic Data Elements

Submatrices

Generating Matrices

Matrix Arithmetic

MATLAB Functions

Programming Features

M-files

Relational and Logical Operators

Columnwise Array Operators

Graphics

Symbolic Toolbox

Help Facility

Conclusions

Bibliography

A. Linear Algebra and Matrix Theory

B. Applied and Numerical Linear Algebra

C. Books of Related Interest

Answers to Selected Exercises