Introduction to Linear Algebra

Linear algebra now rivals or surpasses calculus in importance for people working in quantitative fields of all kinds: engineers, scientists, economists and business people. Gilbert Strang has taught linear algebra at MIT for more than 50 years and the course he developed has become a model for teaching around the world. His video lectures on MIT OpenCourseWare have been viewed over ten million times and his twelve textbooks are popular with readers worldwide. This sixth edition of Professor Strang’s most popular book, Introduction to Linear Algebra, introduces the ideas of independent columns and the rank and column space of a matrix early on for a more active start. Then the book moves directly to the classical topics of linear equations, fundamental subspaces, least squares, eigenvalues and singular values – in each case expressing the key idea as a matrix factorization. The final chapters of this edition treat optimization and learning from data: the most active application of linear algebra today. Everything is explained thoroughly in Professor Strang’s characteristic clear style. It is sure to delight and inspire the delight and inspire the next generation of learners.

Table of Contents

1 Vectors and Matrices

2 Solving Linear Equations Ax = b

3 The Four Fundamental Subspaces

4 Orthogonality

5 Determinants

6 Eigenvalues and Eigenvectors

7 The Singular Value Decomposition (SVD)

8 Linear Transformations

9 Linear Algebra in Optimization

10 Learning from Data

Appendix 1 The Ranks of AB and A + B

Appendix 2 Matrix Factorizations

Appendix 3 Counting Parameters in the Basic Factorizations

Appendix 4 Codes and Algorithms for Numerical Linear Algebra

Appendix 5 The Jordan Form of a Square Matrix

Appendix 6 Tensors

Appendix 7 The Condition Number of a Matrix Problem

Appendix 8 Markov Matrices and Perron-Frobenius

Appendix 9 Elimination and Factorization

Appendix 10 Computer Graphics

About the Author

Gilbert Strang has been teaching Linear Algebra at Massachusetts Institute of Technology (MIT) for over fifty years. His online lectures for MIT’s OpenCourseWare have been viewed over ten million times. He is a former President of the Society for Industrial and Applied Mathematics and Chair of the Joint Policy Board for Mathematics. Professor Strang is the author of twelve books.