Linear Algebra for Everyone: (The Gilbert Strang Series)

This book by Gilbert Strang, author of the widely-used Introduction to Linear Algebra, presents a ``new start'' in teaching and learning linear algebra, a subject that is increasingly important in all quantitative disciplines. Working with small matrices of integers, students can see dependent columns and the rank of $A$ and its column space. This is a big step toward the four fundamental subspaces -- a widespread success in teaching linear algebra. The new start makes linear algebra more approachable to students with a wide range of backgrounds. The next step is the column-row factorization $A = CR$ with independent columns in $C$. Combinations of those columns produce all columns in $A$ -- this is matrix multiplication by $R$. The text goes on to solve $Ax = b$, to orthogonal bases, to subspaces and linear transformations, always based on examples. The final steps are eigenvalues and singular values, with a dedicated code to compress images. The last chapter is entirely optional: linear algebra in deep learning and AI. The text features many illustrative examples and exercises, and video lectures to accompany the book are available via MIT OpenCourseWare. The author's site, contains additional sample material and an instructor's manual.

Table of Contents:
Preface; 1. Vectors and Matrices; 2. Solving Linear Equations Ax = b; 3. The Four Fundamental Subspaces; 4. Orthogonality; 5. Determinants and Linear Transformations; 6. Eigenvalues and Eigenvectors; 7. The Singular Value Decomposition (SVD); 8. Learning from Data; Appendix 1. The Ranks of AB and A + B; Appendix 2. Eigenvalues and Singular Values: Rank One; Appendix 3. Counting Parameters in the Basic Factorizations; Appendix 4. Codes and Algorithms for Numerical Linear Algebra; Appendix 5. Matrix Factorizations; Appendix 6. The Column-Row Factorization of a Matrix; Appendix 7. The Jordan Form of a Square Matrix; Appendix 8. Tensors; Appendix 9. The Condition Number; Appendix 10. Markov Matrices and Perron-Frobenius; Index; Index of Symbols; Six Great Theorems / Linear Algebra in a Nutshell.

About the Author :
Gilbert Strang, Massachusetts Institue of Technology, Cambridge, MA

Review :
'The author certainly makes every effort to explain all the concepts in great detail with well-chosen examples, and he provides a huge number of problems including 'challenge problems' and 'recommended problems'. There are also extensive web resources available.' Peter Giblin, University of Liverpool, The Mathematical Gazette