Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.
Gilbert Strang, Massachusetts Institute of Technology
Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. He is the author of many textbooks and his service to the mathematics community is extensive. He has spent time both as President of SIAM and as Chair of the Joint Policy Board for Mathematics, and has been a member of various other committees and boards. He has received several awards for his research and teaching, including the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (Massachusetts Institute of Technology, 2003) and the Von Neumann Prize Medal (US Association for Computational Mechanics, 2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, and an Honorary Fellow of Balliol College, Oxford.
1. Introduction to vectors
2. Solving linear equations
3. Vector spaces and subspaces
6. Eigenvalues and eigenvectors
7. The singular value decomposition (SVD)
8. Linear transformations
9. Complex vectors and matrices
11. Numerical linear algebra
12. Linear algebra in probability and statistics
Six great theorems/linear algebra in a nutshell.