The sixth edition of Gilbert Strang's best-selling textbook, Introduction to Linear Algebra, continues to combine serious purpose with a gentle touch, providing an accessible and comprehensive guide to the study of linear algebra. Two of the chapters — the first and the last — deserve special mention.

Chapter 1 emphasizes that matrix-vector multiplication Ax produces a linear combination of the columns of
. Those combinations fill the column space of
, and the idea of linear independence is introduced by examples. The result is to see (for small matrices) the ideas of column rank and row rank and a valuable factorization
.

Later chapters (the heart of the book) develop five great factorizations of a matrix, and they are connected to the four fundamental subspaces that students can work with.

Chapter 10 (the closing chapter) — not reached in a first course but so valuable in modern applications — describes the key ideas of Deep Learning. The learning function (built from training data) is piecewise linear with matrix weights. For unseen data, those same weights give an accurate understanding — and every student knows the importance of these ideas.

New to the Sixth Edition:

Two new chapters on applications of linear algebra to vital modern problems of optimization and learning from data.
Expanded coverage of linear transformations and eigenvectors.
Revised treatment of singular value decomposition with a focus on its applications in data analysis and machine learning.
More examples and exercises, helping students to solidify their understanding of the material.
Professor 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 textbooks have been widely adopted.
A publication of Wellesley-Cambridge Press. Distributed within the Americas by the American Mathematical Society.