In Linear Algebra Done Right, Sheldon Axler moves determinants away from the center of the course and focuses the exposition on the structure of linear operators on finite-dimensional vector spaces. The book begins with vector spaces, linear independence, bases, and dimension, then moves on to linear maps, eigenvalues and eigenvectors, inner product spaces, and the spectral theorem. The fourth edition expands its treatment of singular value decomposition, includes a chapter on multilinear algebra, and adds more than 250 exercises.

Teaching, research, and mathematical writing

Axler is professor emeritus in the Department of Mathematics at San Francisco State University. He studied at Princeton and earned a PhD in mathematics from Berkeley in 1975; after a period as a Moore Instructor at MIT, he taught at Michigan State University and joined San Francisco State in 1997, where he chaired the department. He was dean of the College of Science and Engineering from 2002 to 2015. In 1996, he received the Lester R. Ford Award from the Mathematical Association of America for expository writing.

A reference book within a broader body of work

The first edition of Linear Algebra Done Right appeared in 1995, and the text reached its fourth edition in 2024. Axler’s website also offers free videos to accompany the book. His catalog includes works for other levels and in other fields, including Harmonic Function Theory, written with Paul Bourdon and Wade Ramey, and Measure, Integration & Real Analysis. Taken together, his work as an author connects mathematics education with research in functional and complex analysis.