Linear Algebra Done Right

ISBN-10: 0387982582
ISBN-13: 9780387982588
Edition: 2nd 1997 (Revised)
Authors: Sheldon J. Axler
List price: $44.95
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Description: 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  More...

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Book details

List price: $44.95
Edition: 2nd
Copyright year: 1997
Publisher: Springer
Publication date: 2/26/2004
Binding: Paperback
Pages: 251
Size: 8.00" wide x 9.50" long x 0.75" tall
Weight: 1.100
Language: English

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.

Vector Spaces
Finite-Dimensional Vector Spaces
Linear Maps
Polynomials
Eigenvalues and Eigenvectors
Inner-Product Spaces
Operators on Inner-Product Spaces
Operators on Complex Vector Spaces
Operators on Real Vector Spaces
Trace and Determinant

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