# Linear Algebra Done Right

• Sheldon Axler

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xvii
2. Sheldon Axler
Pages 1-26
3. Sheldon Axler
Pages 27-49
4. Sheldon Axler
Pages 51-116
5. Sheldon Axler
Pages 117-130
6. Sheldon Axler
Pages 131-161
7. Sheldon Axler
Pages 163-202
8. Sheldon Axler
Pages 203-240
9. Sheldon Axler
Pages 241-274
10. Sheldon Axler
Pages 275-294
11. Sheldon Axler
Pages 295-331
12. Back Matter
Pages 333-340

### Introduction

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.

The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

### Keywords

Axler linear algebra adopted textbook dual spaces finite-dimensional spectral theorem linear algebra product spaces quotient spaces vector spaces

#### Authors and affiliations

• Sheldon Axler
• 1
1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA