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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.

This fifth edition contains numerous minor improvements and major additions
Provides a new chapter on singular values and singular vectors, as well as a revised chapter on computing in linear algebra
A dedicated and active website offers solutions to exercises, new exercises from several sources, and codes in MATLAB, Julia, and Python



Table of Contents

1. Introduction to vectors
2. Solving linear equations
3. Vector spaces and subspaces
4. Orthogonality
5. Determinants
6. Eigenvalues and eigenvectors
7. The singular value decomposition (SVD)
8. Linear transformations
9. Complex vectors and matrices
10. Applications
11. Numerical linear algebra
12. Linear algebra in probability and statistics
Matrix factorizations
Index
Six great theorems/linear algebra in a nutshell.