Introduction to vectors -- Solving linear equations -- Vector spaces and subspaces -- Orthogonality -- Determinants -- Eigenvalues and eigenvectors -- The singular value decomposition (SVD) -- Linear transformations -- Complex vectors and matrices -- Applications -- Numeral linear algebra -- Linear algebra in probability & statistics -- Matrix factorizations -- Index -- Six great theorems, linear algebra in a nutshell.

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.