Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang’s emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

Written by a professor at MIT, this textbook describes methods for solving linear equations using Gaussian elimination, vector spaces, orthogonality, and determinants, then addresses the challenge of finding eigenvalues and eigenvectors. The term “applications” in the title refers more to the general utility of matrices for advanced mathematical analysis than to an abundance of specific examples. The fourth edition adds new problems and explores interior point methods in the last chapter.

Salient Features

- The exercise sets in the book have been extensively updated. They feature many new problems from Professor Strang’s long experience.
- New coverage of the Singular Value Decomposition has been added to the text.
- A second color has been added to the illustrations and boxes, many of which are new.
- Includes an optional section on the Fast Fourier Transform.
- Students discover how this outstanding algorithm fits into linear algebra and introduces complex numbers.
- Recognizes what the computer can do in linear algebra, without being dominated by it.

2. Vector Spaces.

3. Orthogonality.

4. Determinants.

5. Eigenvalues and Eigenvectors.

6. Positive Definite Matrices.

7. Computations with Matrices.

8. Linear Programming and Game Theory.

Appendix A: Computer Graphics.

Appendix B: The Jordan Form.

References.

Solutions to Selected Exercises.

Index.

REVIEW