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Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) Paperback – 17 Mar 2003


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Product details

  • Paperback: 336 pages
  • Publisher: Dover Publications Inc.; 2nd Revised edition edition (17 Mar 2003)
  • Language: English
  • ISBN-10: 0486663280
  • ISBN-13: 978-0486663289
  • Product Dimensions: 1.9 x 14 x 22.2 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 316,859 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Format: Paperback Verified Purchase
Although the name of the book is Matrices and Linear Transformations, while the author also bring a broader view in algebra, and this offer an introduction for people who want know more in the subject.
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2 of 3 people found the following review helpful By John M. Ford TOP 500 REVIEWER on 10 Jun 2011
Format: Paperback
Charles Cullen's original goal was to "provide a text, requiring a minimum number of prerequisites, which would enable me, in a one-term course, to cover...linear algebra and matrix theory." This volume does so in the first five chapters and continues with four additional chapters designed to support a second term. He suggests as background "only" an introductory course in calculus and analytic geometry.

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.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 19 reviews
61 of 63 people found the following review helpful
Supreme intro to advanced linear algebra and matrix analysis 15 July 2003
By Sweetcheeks McMuffin - Published on Amazon.com
Format: Paperback
Charles Cullen deserves to pat himself on the back for this one. The first three chapters are the meat of the book which review or, possibly to some, introduce the fundamentals of linear algebra (matrices, vector spaces, and determinants.)
After firmly laying down a foundation from which to work with, Cullen does a remarkable job explaining linear transformations and eigenvalues and eigenvectors (although, some basic calculus is assumed known).
After introducing matrix similarity and Jordan-canonical form, Cullen dabbles in polynomial matrices and more similarity with divisor theorems and polynomial matrix canonical form.
Finally, rounding third plate are an intro into formal matrix analysis (in which some upper-level, although not necessarily advanced, calculus is necessary) and numerical methods. Although these two chapters only encompass about 35 pages total, they do offer a solid foundation for further study.
I recommend this book as it breaks a lot of steps involving matrix calculations down and allows the reader to not only understand how, but why.
36 of 38 people found the following review helpful
Matrices Made Plain 18 Oct 2010
By John M. Ford - Published on Amazon.com
Format: Paperback Verified Purchase
Charles Cullen's original goal was to "provide a text, requiring a minimum number of prerequisites, which would enable me, in a one-term course, to cover...linear algebra and matrix theory." This volume does so in the first five chapters and continues with four additional chapters designed to support a second term. He suggests as background "only" an introductory course in calculus and analytic geometry.

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.
39 of 42 people found the following review helpful
Linear algebra is fun 3 Dec 2003
By A Customer - Published on Amazon.com
Format: Paperback
So many math books take a relatively simple topic and with the use of horrible notation and confused english, convert it to something esoteric and complicated. This book, however, is anything but that. It involves mathematical rigor, covers a broad range of topics and has answers to selected problems at the back which for a math book, works real well for me. Besides you can't argue with the price.
This book never leaves my desk, recommended strongly.
15 of 15 people found the following review helpful
An excellent linear algebra book 26 Sep 2008
By Chase J. Valiente - Published on Amazon.com
Format: Paperback Verified Purchase
This book is concise and possesses a great deal of information on matrices. I had to buy $100+ book for a upper division linear algebra class and it sucked; it contained in 300 very cluttered and long winded pages what this book accomplishes in a little over a hundred pages with far greater depth. It's a highly affordable book and quite well written, which, I guess, is why they don't use this book to teach linear algebra in a 'modern' classroom.
27 of 32 people found the following review helpful
Advanced undergraduate reference 6 July 2005
By Peter Kwok - Published on Amazon.com
Format: Paperback
This book is in its second edition. But it was copyrighted 1972, not 1990. Its original price was $8.95. Perhaps Dover increased its price to $14.95 in the latest printing. But I still think Amazon was a bit misleading there.

In any case, this is an undergraduate level reference book with proofs on Laplace Expansion, Cramer's Rule, Jordan Canonical Form, Cayley-Hamilton Theorem, and other stuff that you see it proved once and never want to see it again. The last section even covers numerical methods on matrices. All in all, it got a good mix of rigor and practicality for a book of its kind.
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