- Tapa blanda: 336 páginas
- Editor: Dover Publications Inc.; Edición: Revised (17 de marzo de 2003)
- Colección: Dover Books on Mathematics
- Idioma: Inglés
- ISBN-10: 0486663280
- ISBN-13: 978-0486663289
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº316.268 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
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Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) (Inglés) Tapa blanda – 17 mar 2003
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Undergraduate-level introduction to linear algebra and matrix theory deals with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Also spectral decomposition, Jordan canonical form, solution of the matrix equation AX=XB, and over 375 problems, many with answers. "Comprehensive." ― Electronic Engineer's Design Magazine.
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The first chapter introduces basic matrix operations such as addition, multiplication, transposition and inversion. Chapter 2 covers vector spaces and the concepts of linear independence and rank. Chapters 3 and 4 introduce and elaborate matrix determinants and linear transformations. Chapter 5 develops the Jordan canonical form using invariant subspaces and direct sum decompositions. Chapters 6 and 7 take an alternative path to explaining the Jordan canonical form. Chapters 8 and 9 use concepts and tools from previous chapters to introduce matrix analysis and numerical analysis.
I bought this book for an online matrix algebra course when I found the required text, Matrix Algebra: An Introduction, less than helpful. Even though the course text was targeted toward social scientists like myself, its explanations and formula derivations were less helpful than its examples. I found Cullen's book and it got me through the course. In addition to clear explanations, practice exercises with answers, and helpful organization, it was also less expensive and covered more material.
I recommend this book to those needing a refresher in matrix methods or approaching them for the first time.
The book is very comprehensive. The author says it's intended for a one-semester course but then qualifies that; the whole book would take two semesters at most universities. The book is also very rigorous. This is great, depending on what you're looking for. If you want no-compromise, thorough learning, you'll get it, but you'll have to work for it. I mean serious work.
The book says it has little in the way of prerequisites. That's true in a strict sense, but in fact I think to use this book you need a certain amount of mathematical sophistication. A basic "proofs" book might be a good companion or even a prior study. The author doesn't hold back on formalism and use of notation, and some level of comfort with this is necessary.
That doesn't mean the book is overly academic, obscure, or unclear. It's none of those things. But what it does is demand a lot on the part of the student. You absolutely must take the time to learn everything as it's presented. There isn't much in the way of repetition and second chances, although there are detailed examples which are quite helpful. Working the problems (there are a few solutions given) is also essential, and I'd use one of those Schaum books (or similar) to supplement the problems and examples.
The exacting rigor at times obscures practical application; the presentation of determinants, for instance, is not at all what I'm used to--- but that said, it gave me a different and greater level of understanding.
If you're looking to study more advanced, abstract math, the first five chapters are crucial and you might want to look at the seventh chapter and maybe some other material. The author gives good suggestions in the introduction.
This, of course, is an older book, but it remains very relevant. You can certainly use it for self-study if you use a supplement or two and if you're willing to put in the effort. If you want a light and happy overview that doesn't demand intellectual effort, look elsewhere. If you really want to master the material, consider this book. It isn't a classic text for nothing.
My only complaint is that I purchased the Kindle edition and, being replete with equations and mathematical symbols that are tiny images, it is very hard to read because they don't scale with the text.
I would recommend purchasing the paper version and not the Kindle version.
He gives clear and careful explanations, including numbered definitions of key concepts. There are also plenty of examples and exercises.
For a comprehensive introduction to linear algebra, there's no better book than David C. Lay's Linear Algebra and Its Applications (4th Edition). But for an overview or a quick review, this is a better book than Lay. I really like it.
(The Lay book has the advantage of being available for the Kindle app on the iPad. The Cullen book isn't. On the other hand, the e-Book version of Lay is slow and clunky, so it's obviously not optimized for the e-Book format.)