- Paperback: 266 pages
- Publisher: Springer; 2nd ed. 1997. Corr. 7th printing edition (July 18 1997)
- Language: English
- ISBN-10: 0387982582
- ISBN-13: 978-0387982588
- Product Dimensions: 23.4 x 19.5 x 1.5 cm
- Shipping Weight: 499 g
- Average Customer Review: 4.1 out of 5 stars See all reviews (21 customer reviews)
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Amazon Bestsellers Rank:
#54,907 in Books (See Top 100 in Books)
- #52 in Books > Science > Mathematics > Pure Mathematics > Algebra
- #66 in Books > Science > Mathematics > Pure Mathematics > Calculus
- #75 in Books > Reference > Dictionaries & Thesauruses > Science
- See Complete Table of Contents
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Product Details |
Product Description
Review
From the reviews: ZENTRALBLATT MATH "This second edition of an almost determinant-free, none the less remarkably far-reaching and didactically masterly undergraduate text on linear algebra has undergone some substantial improvements. First of all, the sections on selfadjoint operators, normal operators, and the spectral theorem have been rewritten, methodically rearranged, and thus evidently simplified. Secondly, the section on orthogonal projections on inner-product spaces has been extended by taking up the application to minimization problems in geometry and analysis. Furthermore, several proofs have been simplified, and incidentally made more general and elegant (e.g., the proof of the trigonalizability of operators on finite-dimensional complex vector spaces, or the proof of the existence of a Jordan normal form for a nilpotent operator). Finally, apart from many other minor improvements and corrections throughout the entire text, several new examples and new exercises have been worked in. However, no mitigation has been granted to determinants. Altogether, with the present second edition of his text, the author has succeeded to make this an even better book." AMERICAN MATHEMATICAL MONTHLY "The determinant-free proofs are elegant and intuitive." CHOICE "Every discipline of higher mathematics evinces the profound importance of linear algebra in some way, either for the power derived from its techniques or the inspiration offered by its concepts. Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de forces in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose. Students with a view towards applied mathematics, analysis, or operator theory will be well served. The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library." ZENTRALBLATT MATH "Altogether, the text is a didactic masterpiece." From the reviews of the second edition: S. Axler Linear Algebra Done Right "The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library."--CHOICE "A didactic masterpiece."--ZENTRALBLATT MATH "This book can be thought of as a very pure-math version of linear algebra ! . it focuses on linear operators, primarily in finite-dimensional spaces ! . Axler has come up with some very slick proofs of things that ! makes the book interesting for mathematicians. The book is also very clearly written and fairly leisurely. ! Axler concentrates on the properties of linear operators, and doesn't introduce other concepts unless they're really necessary." (Allen Stenger, The Mathematical Association of America, December, 2010)
Book Description
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on 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 has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, 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. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Inside This Book
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First Sentence
You should already be familiar with the basic properties of the set R of real numbers. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
You should already be familiar with the basic properties of the set R of real numbers. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
5.0 out of 5 stars
the only book you need for linear algebra,
Amazon Verified Purchase(What's this?)
This review is from: Linear Algebra Done Right (Paperback)
get this book if your serious about math or physics. its easy to understand, formulated quite generally (for example the author uses vector spaces defined over arbitrary fields, not just R or C), and lots of examples (possibly too many examples). this book in conjunction with a good text on the computational/algorithmic aspects of matrices can definitely serve as an adequate undergraduate-level training in linear algebra and its applications. despite its horrid title, this would be a beautiful addition to any students bookshelf.
4.0 out of 5 stars
Good buy at the given low price,
By
This review is from: Linear Algebra Done Right (Paperback)
Linear Algebra Done Right is a decent undergraduate, introductory Linear Algebra book. The ideas are presented intuitively and elegantly, and the book covers a great deal of ground. This being said, the book has some definite drawbacks. For one, the author's discussion of determinants in the last chapter is pathetic. I agree with this view that determinants should be avoided, and in their place more intuitive, geometric ideas should be used. That being said, a good understanding of determinants is crucial for mathematical maturity, and they should still be covered in some detail. Some of his 'proofs' relating to determinants and change of bases in the last chapter are an assault on the senses (ugly, poorly written, etc.), and should be discarded post haste. Overall though, a good introductory undergraduate text, worth the price.
5.0 out of 5 stars
Elegant theoretical presentation of linear algebra,
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This review is from: Linear Algebra Done Right (Paperback)
This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent. The student has perhaps taken a linear algebra course designed for engineers and scientists. Such a student is comfortable reading mathematics and writing proofs. It is meant to be read and re-read until the ideas are absorbed. The exercises are relatively easy and no answers are provided. With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra. The price is right. This could be a very useful purchase even if it's not assigned as a text.
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