Matrix Analysis and Applied Linear Algebra

This second edition has been almost completely rewritten to create a textbook designed so instructors can determine the degree of rigor and flexible enough for a one- or two-semester course. The author achieves this by increasing the level of sophistication as the text proceeds from traditional first principles in the early chapters to theory and applications in the later ones, and by ensuring that material at any point is not dependent on subsequent developments. While theorems and proofs are highlighted, the emphasis is on applications. The author provides carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow. An accompanying book, Matrix Analysis and Applied Linear Algebra, Second Edition, Study and Solutions Guide, contains complete solutions and discussions of each exercise; and historical remarks that focus on the personalities of the individuals who created and contributed to the subject’s development. This book is designed for use in either a one- or two-term linear algebra course. It can also serve as a reference to anyone who needs to use or apply linear algebra.

Table of Contents

1. The Language of Linear Algebra

2. Systems, Elimination, and Echelon Forms

3. Eigensystem Basics

4. Vector Spaces

5. Inner Product Spaces and Fourier Expansions

6. Eigenvalue Continuity and Computations

7. Perron–Frobenius and Nonnegative Matrices

8. Matrix Analysis via Resolvent Calculus

9. Appendix: An Overview of Determinants

About the Author

Carl D. Meyer is Emeritus Professor of Mathematics at North Carolina State University, and he is a SIAM Fellow.