Linear Algebra Done Right

Sheldon Axler, Professor Emeritus of the Mathematics Department at San Francisco State University, has authored many well-received books including Linear Algebra Done Right (in four editions) Measure, Integration & Real Analysis (Open Access) Precalculus: A Prelude to Calculus, Algebra & Trigonometry (in three editions)College Algebra Harmonic Function Theory (in two editions).Axler has served as Editor-in-Chief of the Mathematical Intelligencer and Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. He is a Fellow of the American Mathematical Society and has been a recipient of numerous grants from the National Science Foundation.

“Each section is followed by a set of original exercises with varying levels of difficulty, designed to thoroughly reinforce the concepts presented within that section. This book can be a valuable resource for linear algebra courses where a determinant free approach to the initial development of the subject is deemed pedagogically appropriate. … the textbook offers a rigorous development of linear algebra over R and C with a unique treatment of determinants.” (Peteris Daugulis, Mathematical Reviews, June, 2025)

• Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces.- 2. Finite-Dimensional Vector Spaces.- 3. Linear Maps.- 4. Polynomials.- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces.- 6. Inner Product Spaces.- 7. Operators on Inner Product Spaces.- 8. Operators on Complex Vector Spaces.- 9. Operators on Real Vector Spaces.- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.