Linear Algebra Done Right

Sheldon Axler

Springer, Jul 18, 1997 - Mathematics - 251 pages

This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents--without having defined determinants--a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. 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. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

What people are saying

Review: Linear Algebra Done Right

User Review  - Peteris Erins - Goodreads

Not particularly enlightening. Unassuming yet thorough coverage of finite vector spaces with only a brief mention of the infinite.

Review: Linear Algebra Done Right

User Review  - Kevin - Goodreads

A much, much better coverage of linear algebra than the book my undergrad class used. As many others have noted, it largely avoids the use of matrices and determinants to focus on the purely algebraic ...

About the author

Axler-San Francisco State University

Bibliographic information

• Title: Linear Algebra Done Right; Undergraduate Texts in Mathematics, ISSN 0172-6056
• Author: Sheldon Axler
• Edition: 2, illustrated, reprint
• Publisher: Springer, 1997
• ISBN: 0387982582, 9780387982588
• Length: 251 pages
• Subjects: Mathematics / Algebra / Linear