oder
Loggen Sie sich ein, um 1-Click® einzuschalten.
oder
Mit kostenloser Probeteilnahme bei Amazon Prime. Melden Sie sich während des Bestellvorgangs an.
Jetzt eintauschen
und EUR 7,75 Gutschein erhalten
Eintausch
Alle Angebote
Möchten Sie verkaufen? Hier verkaufen
Der Artikel ist in folgender Variante leider nicht verfügbar
Keine Abbildung vorhanden für
Farbe:
Keine Abbildung vorhanden

 
Den Verlag informieren!
Ich möchte dieses Buch auf dem Kindle lesen.

Sie haben keinen Kindle? Hier kaufen oder eine gratis Kindle Lese-App herunterladen.

Linear Algebra Done Right (Undergraduate Texts in Mathematics) [Englisch] [Taschenbuch]

Sheldon Axler
4.3 von 5 Sternen  Alle Rezensionen anzeigen (3 Kundenrezensionen)
Preis: EUR 36,33 kostenlose Lieferung. Siehe Details.
  Alle Preisangaben inkl. MwSt.
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Auf Lager.
Verkauf und Versand durch Amazon. Geschenkverpackung verfügbar.
Lieferung bis Freitag, 22. August: Wählen Sie an der Kasse Morning-Express. Siehe Details.

Weitere Ausgaben

Amazon-Preis Neu ab Gebraucht ab
Gebundene Ausgabe EUR 63,72  
Taschenbuch EUR 36,33  

Kurzbeschreibung

2. Juni 2010 0387982582 978-0387982588 2nd ed. 1997. Corr. 7th printing 2004
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.

Hinweise und Aktionen

  • Studienbücher: Ob neu oder gebraucht, alle wichtigen Bücher für Ihr Studium finden Sie im großen Studium Special. Natürlich portofrei.


Wird oft zusammen gekauft

Linear Algebra Done Right (Undergraduate Texts in Mathematics) + Analysis 1 (Springer-Lehrbuch)
Preis für beide: EUR 61,28

Die ausgewählten Artikel zusammen kaufen
  • Analysis 1 (Springer-Lehrbuch) EUR 24,95

Kunden, die diesen Artikel gekauft haben, kauften auch


Produktinformation

  • Taschenbuch: 272 Seiten
  • Verlag: Springer New York; Auflage: 2nd ed. 1997. Corr. 7th printing 2004 (2. Juni 2010)
  • Sprache: Englisch
  • ISBN-10: 0387982582
  • ISBN-13: 978-0387982588
  • Größe und/oder Gewicht: 1,5 x 19,2 x 23,1 cm
  • Durchschnittliche Kundenbewertung: 4.3 von 5 Sternen  Alle Rezensionen anzeigen (3 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 78.471 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
  • Komplettes Inhaltsverzeichnis ansehen

Mehr über den Autor

Entdecken Sie Bücher, lesen Sie über Autoren und mehr

Produktbeschreibungen

Pressestimmen

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)

Synopsis

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.


Welche anderen Artikel kaufen Kunden, nachdem sie diesen Artikel angesehen haben?


In diesem Buch (Mehr dazu)
Einleitungssatz
You should already be familiar with the basic properties of the set R of real numbers. Lesen Sie die erste Seite
Mehr entdecken
Wortanzeiger
Ausgewählte Seiten ansehen
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
Hier reinlesen und suchen:

Eine digitale Version dieses Buchs im Kindle-Shop verkaufen

Wenn Sie ein Verleger oder Autor sind und die digitalen Rechte an einem Buch haben, können Sie die digitale Version des Buchs in unserem Kindle-Shop verkaufen. Weitere Informationen

Kundenrezensionen

3 Sterne
0
2 Sterne
0
1 Sterne
0
4.3 von 5 Sternen
4.3 von 5 Sternen
Die hilfreichsten Kundenrezensionen
1 von 1 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Superb. The best book on the subjet. 1. Februar 2000
Von Ein Kunde
Format:Taschenbuch
I've seen many linear algebra books and this is by far the best treatment of them all. After going through this book one wonder why most linear algebra presentations don't follow Axler's sound and more reasonable approach. It leaves Hoffman & Kunze in the dust (although you may still want to hang on to Hoffman since it contains some material not found in Axler).
Not only is Axler's approach sound, but his writing is very lucid and clear as well. You will never leave a proof feeling unsatisfied or confused; it almost reads like a book. I wish all math books were written this way.
My only gripe with the book is the lack of solutions to the problems. Those who use the book for self-study will feel particular frustrated in this regard. I hope some effort is taken to assuage this problem in future editions. Also, more material on linear functionals and multilinear mappings (tensors) would be nice.
In summary, this is an outstanding book; I highly recommend it.
War diese Rezension für Sie hilfreich?
4.0 von 5 Sternen ``Done right'' is right 8. Oktober 1998
Von Ein Kunde
Format:Taschenbuch
A brief book on linear algebra that develops the theory by emphasizing vector spaces and linear maps; this leads to clearer, more elegant proofs than the traditional, matrix-based approach. This approach manages to be both more lucid and more abstract.
Among the many fine features of this book are the author's marginal notes highlighting important points, commenting on strategy, and mentioning other names that a concept may go by (e.g., an injective mapping is also known as one-to-one, this is quite useful for beginning students).
War diese Rezension für Sie hilfreich?
4.0 von 5 Sternen Excellent for a second course in Linear Algebra 26. April 1998
Von Ein Kunde
Format:Taschenbuch
The book does a better job of explaining what is happening at the heart of linear spaces and linear transformations than most. This is mostly due to the fact that linear maps and operators are used more often that matrices in the proofs, and that determinants are relegated to the end of the book. Overall a very good bare bones, gives you what you need book.
War diese Rezension für Sie hilfreich?
Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)
Amazon.com: 4.0 von 5 Sternen  91 Rezensionen
112 von 117 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Clean and elegant, but not quite what the doctor ordered 1. November 2005
Von Bob - Veröffentlicht auf Amazon.com
Format:Taschenbuch
I have used this text for a beginning graduate course in linear algebra, mostly because I prefer its treatment of eigenvalues and eigenvectors over Hoffman and Kunze, and it sticks to the basics: complex scalars. It also has a good treatment of inner product spaces. The basic concepts and theorems are indeed presented cleanly and elegantly. Its use of linearly independent sequences (rather than sets) is a little nonstandard (what if the set of vectors is infinite?) but the adjustment is minor. Two things though I found treated in a less than desirable fashion: He pretends that we don't know about matrices, doesn't want to develop the machinery, and the treatment of coordinate vectors and matrix representations suffers. Students also get no sense of how to compute the solution of concrete vector space problems, which is easily done once the theory is established, and which is an essential skill to have after a second course in linear algebra. I have to give them supplementary notes. Second, the treatment of determinants suffers, apparently for ideological/political reasons. I think students deserve a straightforward development of determinants simply because that theory is widely used in applications, in engineering, and in discrete mathematics, and it has its own beauty. It is not hard to do, and I do it myself from notes, adapted from the treatment of Hoffman and Kunze. Now that undergraduate linear algebra courses have in many places dropped any substantial theorem-proving component, students need a serious course in linear algebra which can take them, e.g. all the way into Jordan form. There are not many good books for this, and this text does a good job with the basics without overkill on the abstraction, so I use it despite the drawbacks mentioned above.
70 von 75 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Simply Amazing 4. Juli 2003
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format:Taschenbuch
I was very much the typical person in the target audience of this. I was a computer science major and I had a semester of linear algebra where all I learned how to solve Ax = b. Then, I happened to pick up Axler one winter evening because the title looked intriguiging. That day changed my life.
Now, I'm a pure math major and Axler is the reason. The exposition is clean and very elegant. By minimizing the use of matrices in his proofs, he presents the subject of linear algebra as an elegant piece of mathematics rather than a subject "spoilt" by applications. He starts with a study of vector spaces and then moves onto transformations, eigenvalues, inner product spaces, etc. all the way upto the jordan form. All along, the use of matrices in minimal. In fact, he introduces them quite late in the book just as a convenient notation and nothing else. This is an admirable aspect because it simplies a lot of the proofs. The proof that every linear operator over a finite-dimensional vector space has an eigenvalue is breathtakingly short and simple. He uses determinants in the last chapter of the book and there too, does an excellent job. (although the point of writing this book was NOT to use determinants, his exposition about determinants is itself one of the best ones I've seen).
Get this book if you wish to understand the theory. It's a typical higher level math text - definition, theorem, proof, exercises (most of which are theorems). If you like math, you won't regret this.
67 von 72 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Thought Provoking 26. September 2007
Von Salviati - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
I have no doubt that this is one of the most thought provoking math books that I have come across. I used this book for a linear algebra course last fall '07 and I learned a ton. Specifically about the structure of vector spaces and linear operators. However, the most important function that this book serves is to move students towards the methodology of mathematics, which means proof construction and counter examples. It also trains students to let go of their intuitions. But you can not self-study this book, there are no answers and more importantly the structure of the course begs for instruction. I would recommend before taking this course doing what i didn't do and have had to do since, make sure you have your first course of linear algebra solidly under your belt, and that doesn't mean having gotten an A in the prior class is sufficient. Go through the most difficult proof driven exercises in your first text, that should serve as practice for easiest homework problems in this book.

All that said, there are serious limitations to this book. It would be nice if the author worked out 1 comprehensive semi-difficult exercise in each chapter of the text. While struggling to solve the problems can be enlightening, there is only so many times I can read the same sections over and over again, looking for some insight from the kiddie exercises provided by the author. It would also help if some of the kiddie exercises were accompanied with graphs, especially when describing the sums of vector spaces. Sometimes a picture is worth a thousand words - sometimes!
72 von 81 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Superb. The best book on the subjet. 1. Februar 2000
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format:Taschenbuch
I've seen many linear algebra books and this is by far the best treatment of them all. After going through this book one wonder why most linear algebra presentations don't follow Axler's sound and more reasonable approach. It leaves Hoffman & Kunze in the dust (although you may still want to hang on to Hoffman since it contains some material not found in Axler).
Not only is Axler's approach sound, but his writing is very lucid and clear as well. You will never leave a proof feeling unsatisfied or confused; it almost reads like a book. I wish all math books were written this way.
My only gripe with the book is the lack of solutions to the problems. Those who use the book for self-study will feel particular frustrated in this regard. I hope some effort is taken to assuage this problem in future editions. Also, more material on linear functionals and multilinear mappings (tensors) would be nice.
In summary, this is an outstanding book; I highly recommend it.
18 von 19 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Forgive him for the title 28. Februar 2011
Von Raman - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
What an awful title. I guess Sheldon Axler decided on the ungrammatical "Linear Algebra Done Right" to avoid "Linear Algebra Done Properly" or something similar, which would have sounded intolerably arrogant. He justifies this title repeatedly by rather obnoxiously flaunting his determinant-free proof that operators on complex (or real, odd-dimensional) vector spaces have an eigenvalue. (It's pretty cool, but I've seen cooler constructions, and I'm not even a mathematician.) He also often makes other snarky jabs at the unnamed body of traditional linear algebra texts.

Read the book, and you will forgive him on all counts.

Other reviewers have already been thorough in their praise/criticism of Axler's elegant exposition that deprecates matrices and determinants. The highlight in my view is how Axler cleans up proofs by simplifying notation and carefully abstracting common algorithms into lemmas (like 2.4, his Linear Dependence Lemma) that are used over and over. This greatly improves readability and promotes the development of intuition. Some of his nonstandard choices of notation are used to such great pedagogical effect that they seem to threaten to redefine what is standard. The prose is correspondingly clear, concise, and full of useful motivation for difficult points. The formatting is impeccable - definitions, equations, inequalities, and theorems/lemmas are all given a uniform numbering system, making them easy and unambiguous to cite. Subsidiary comments are relegated to the margins of the book, keeping the main line of exposition free of digressions. The text is quite shockingly free of errors. Finally, the layout has a clean but cheerful flower-power look that reminds the reader that math is about beauty and fun - not just intimidating formalism.

Axler's refusal to refer directly to others for inspiration (he seemingly proudly omits a bibliography) does cause some warts. For instance, when looking at orthogonal projections for optimization, he asks the reader to do inner-product gymnastics in polynomial space on [0,1] instead of on [-1,1]. The latter choice gives rise to the all-important Legendre polynomials, whose symmetry properties are much clearer.

Also, while the pristine algebraic presentation was remarkable, I'd have liked to see more geometric insight in places. I got into this book because my undergraduate linear algebra experience, with Apostol Vol. 2, was so frustrating - all of the sweeping and magical structure theorems of self-adjoint operators and so forth seemed to reduce to incomprehensible index-pushing. For me, what finally cleared up these notions to me was drawing, on graph paper, the fate of vectors in R^2 under various linear operators. This was not in the book, but Axler's inclusion of the theory of polar and singular-value decompositions did give some important tools to help unravel these beautiful but elusive issues. Finally, the crystal clarity of the exposition rolls off in Chapters 8 and 9 when getting into the structure theory of general operators on real and complex vector spaces. The symbols get more abstruse, and the arguments get more murky. But I've never seen another author make anything but a mess of, say, the proof of Jordan form. It is hard stuff, and it is not fair to be too hard on authors for failing to make it look easy.

The end-of-chapter problems are abundant enough to give a good feel for the material, with an appropriate range of difficulties for an advanced undergraduate book. There are enough of the routine computations and simple proofs that familiarize readers with the new machinery they are learning, but at least a proof or two in each chapter require creative constructions to complete. I just finished the last of the 224 problems, a task that took me five years' worth of sporadic effort in my free time and vacations as a high school math teacher and then as a graduate student in chemistry. A few problems took me the better part of a year to figure out, though this was without the benefit of collaboration. I found the equivalent of at one sequence of problems (problems 6-8 in Chapter 6) as a starred problem in a graduate functional analysis text. I consider myself a good but not award-winning math student, so this indicates that the problems are consistently tractable but can get pretty tough in places. Axler does not mark his most difficult problems as such; for the teacher assigning Axler's problems for a course, then, it is imperative to work through the problems beforehand.

All told, this is quite a remarkable book. I now feel like I understand linear algebra, something I couldn't say when I first studied the subject eight years ago. The title does not do it justice.
Waren diese Rezensionen hilfreich?   Wir wollen von Ihnen hören.
Kundenrezensionen suchen
Nur in den Rezensionen zu diesem Produkt suchen

Kunden diskutieren

Das Forum zu diesem Produkt
Diskussion Antworten Jüngster Beitrag
Noch keine Diskussionen

Fragen stellen, Meinungen austauschen, Einblicke gewinnen
Neue Diskussion starten
Thema:
Erster Beitrag:
Eingabe des Log-ins
 

Kundendiskussionen durchsuchen
Alle Amazon-Diskussionen durchsuchen
   


Ähnliche Artikel finden


Ihr Kommentar