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 all the qualities 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 - 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.