Linear Algebra Done Right

  • Sheldon Axler

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

Table of contents

  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 163-202
  7. Sheldon Axler
    Pages 203-240
  8. Sheldon Axler
    Pages 241-274
  9. Sheldon Axler
    Pages 275-294
  10. Sheldon Axler
    Pages 295-331
  11. Back Matter
    Pages 333-340

About this book


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.


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

Bibliographic information

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