Linear Algebra Done Right / Edition 2

Linear Algebra Done Right / Edition 2

3.6 8
by Sheldon Axler
     
 

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.… See more details below

Overview

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.

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Product Details

ISBN-13:
9780387982588
Publisher:
Springer New York
Publication date:
07/18/1997
Series:
Undergraduate Texts in Mathematics Series
Edition description:
2nd ed. 1997. Corr. 7th printing 2004
Pages:
251
Sales rank:
828,451
Product dimensions:
0.58(w) x 7.50(h) x 9.25(d)

Related Subjects

Table of Contents

Preface to the Instruction
Preface to the Student
Acknowledgments
Ch. 1Vector Spaces1
Ch. 2Finite-Dimensional Vector Spaces21
Ch. 3Linear Maps37
Ch. 4Polynomials63
Ch. 5Eigenvalues and Eigenvectors75
Ch. 6Inner-Product Spaces97
Ch. 7Operators on Inner-Product Spaces127
Ch. 8Operators on Complex Vector Spaces163
Ch. 9Operators on Real Vectors Spaces193
Ch. 10Trace and Determinant213
Symbol Index247
Index249

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