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Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) [Paperback]

Charles G. Cullen
4.6 out of 5 stars  See all reviews (18 customer reviews)

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Book Description

May 1, 1990 0486663280 978-0486663289 2nd
"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine.
This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field.
Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods.
The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 336 pages
  • Publisher: Dover Publications; 2nd edition (May 1, 1990)
  • Language: English
  • ISBN-10: 0486663280
  • ISBN-13: 978-0486663289
  • Product Dimensions: 8.5 x 5.4 x 0.7 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #37,649 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
57 of 59 people found the following review helpful
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.
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33 of 35 people found the following review helpful
4.0 out of 5 stars Matrices Made Plain October 17, 2010
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.
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38 of 41 people found the following review helpful
5.0 out of 5 stars Linear algebra is fun December 3, 2003
By A Customer
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.
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13 of 13 people found the following review helpful
5.0 out of 5 stars An excellent linear algebra book September 25, 2008
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.
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27 of 32 people found the following review helpful
5.0 out of 5 stars Advanced undergraduate reference July 5, 2005
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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9 of 10 people found the following review helpful
5.0 out of 5 stars Clear and concise June 3, 2009
Format:Paperback|Verified Purchase
Matrices and Linear Transformations goes right to the point.
The text is clear and concise and is illustrated by a limited number but very helpful set of examples.
The proof are easy to follow but are rigorous.
This is without a doubt my favorite book about matrices.
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8 of 9 people found the following review helpful
4.0 out of 5 stars Good but perhaps too technical. August 23, 2012
Format:Paperback|Verified Purchase
A great intro book to Matrices and Linear Transformations with tons of depth and great info. Be forewarned however this book is not for the mathematically faint of heart if you're a recent highschool graduate without at least a basic understanding of mathematical signs and symbols (sigma notation, set builder, etc.) you will have a tough time of understanding this book. This is really a serious math textbook and without some significant understanding of how to read math books, you may have some studying to do beforehand. I can say absolutely that this book is not worth your time if you don't know your notation. Otherwise a wholly recommendable book especially for those entering computer graphics/engine design.
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Most Recent Customer Reviews
5.0 out of 5 stars Five Stars
quick delivery
Published 9 days ago by LikeShostakovich
4.0 out of 5 stars Great book - Kindle version presentation problems.
Although published over 40 years ago, this book is well written and organized. The type of information contained in it doesn't expire. Read more
Published 10 days ago by Paul Olson
5.0 out of 5 stars Excellent book
There are many great introductory books on linear algebra and this is one of them.

Linear algebra is such a broad field that different books could cover the subject... Read more
Published 8 months ago by Noah
5.0 out of 5 stars Just got done self studying for Linear Algebra
This book is a very good book for someone wanting to dive into Linear algebra. The author does a massive number of the proofs in the book and is fairly good at explaining the... Read more
Published 11 months ago by Kevin
5.0 out of 5 stars i just love it i just wish to have more time for it
well I'm kind of crazy with math for engineers probably you can call me nerd mathematician and i used to teach math for college and engineer,today my free time is for a good book... Read more
Published 11 months ago by marco
5.0 out of 5 stars another great linear algebra book
I have several books on linear algebra and no two of them attack the topic the same way. This book offers a theoretical bent and convers some of the important theorems not covered... Read more
Published 12 months ago by jibber_jabber
2.0 out of 5 stars Not as clear as some
I prefer references more clearly written and with examples. This was just so-so and I returned it. This book seemed more academically focused and less towards practical... Read more
Published 12 months ago by mc
4.0 out of 5 stars Book of Theorems
This book does an excellent job of proving theorems and providing examples to problems. I will always refer to this book for linear algebra theory. Read more
Published 15 months ago by USNavyUFGator
4.0 out of 5 stars Too troublesome exercise
I am reading this for my self study. This book is easy to understand and good for beginners. I have never read other linear algebra books so I don't know if it is relatively good. Read more
Published 16 months ago by tengu
Published 17 months ago by GRAEME
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