## Table of contents for Visual linear algebra / Eugene A. Herman, Michael D. Pepe, with contributions by Eric P. Schulz.

Bibliographic record and links to related information available from the Library of Congress catalog. Note: Electronic data is machine generated. May be incomplete or contain other coding.

```

CHAPTER 1         Systems of Linear Equations                1

1.1   Solving Linear Systems 2
1.2   Geometric Perspectives on Linear Systems 18
1.3A Solving Linear Systems Using Maple 26
1.3B  Solving Linear Systems Using Mathematica  36
1.4   Curve Fitting and Temperature Distribution-Application  45

CHAPTER 2         Vectors       56

2.1   Geometry of Vectors 57
2.2   Linear Combinations of Vectors 71
2.3   Decomposing the Solution of a Linear System  84
2.4   Linear Independence of Vectors 92
2.5   Theory of Vector Concepts  106

CHAPTER 3         Matrix Algebra          113

3.1   Product of a Matrix and a Vector 114
3.2   Matrix Multiplication  125
3.3  Rules of Matrix Algebra  140
3.4   Markov Chains-Application 147
3.5   Inverse of a Matrix  161
3.6  Theory of Matrix Inverses  175
3.7   Cryptology-Application 180

xviii

CHAPTER 4         Linear Transformations            193

4.1  Introduction to Matrix Transformations 194
4.2  Geometry of Matrix Transformations of the Plane  198
4.3  Geometry of Matrix Transformations of 3-Space 220
4.4  Linear Transformations 232
4.5  Computer Graphics-Application 237

CHAPTER 5         Vector Spaces          255

5.1  Subspaces of Rn 256
5.2   Basis and Dimension 262
5.3  Theory of Basis and Dimension  272
5.4  Subspaces Associated with a Matrix  275
5.5  Theory of Subspaces Associated with a Matrix  285
5.6  Loops and Spanning Trees-Application 289
5.7  Abstract Vector Spaces 297

CHAPTER 6         Determinants          306

6.1  Determinants and Cofactors 307
6.2   Properties of Determinants 311
6.3  Theory of Determinants 322

CHAPTER 7         Eigenvalues and Eigenvectors               328

7.1   Introduction to Eigenvalues and Eigenvectors 329
7.2   The Characteristic Polynomial 343
7.3  Discrete Dynamical Systems-Application  356
7.4  Diagonalization and Similar Matrices 373
7.5  Theory of Eigenvalues and Eigenvectors 389
7.6  Systems of Linear Differential Equations-Application  395
7.7  Complex Numbers and Complex Vectors 407
7.8  Complex Eigenvalues and Eigenvectors 411

CHAPTER 8          Orthogonality          431

8.1  Dot Product and Orthogonal Vectors 432
8.2   Orthogonal Projections in R2 and R3 437
8.3   Orthogonal Projections and Orthogonal Bases in R" 447
8.4  Theory of Orthogonality 456
8.5    Least-Squares Solutions-Application 463
8.6   Weighted Least-Squares and Inner Products on Rn 475
8.7    Approximation of Functions and Integral Inner Products 483
8.8   Inner Product Spaces 496

Appendix A    Glossary of Linear Algebra Definitions 503
Appendix B    Linear Algebra Theorems 510
Appendix C    Advice for Using Maple with Visual Linear Algebra 519
Appendix D    Commands Used in Maple Tutorials 521
Appendix E    Advice for Using Mathematica with Visual Linear Algebra 527
Appendix F   Commands Used in Mathematica Tutorials 530
Appendix G    Answers and Hints for Selected Pencil and Paper Problems 537

Index         545

```
Library of Congress Subject Headings for this publication: