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.

1. Vectors and matrices; 2. Solving linear equations; 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 numbers of a matrix problem; Appendix 8. Markov matrices and Perron-Frobenius; Appendix 9. Elimination and factorization; Appendix 10. Computer graphics; Index of equations; Index of notations; Index.