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“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.
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Book ID Asin: B00CWR4L86
Book Title: Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics)
Book Author: Charles G. Cullen
Book Format and Price:
Book Format Name: Kindle
Book Format Price: $9.99
Book Format Name: Hardcover
Book Format Price: $9.50
Book Format Name: Paperback
Book Format Price: $9.83-$20.93
Book Price: $13.37
Book Category: Kindle Store, Kindle eBooks, Science & Math and unknown
Book Rating: 65 ratings
Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) by Charles G. Cullen Book Review
Name: Robert J. Newell
Rating: 5.0 out of 5 stars
Title: Rigorous, demanding, and rewarding
Date: Reviewed in the United States on May 22, 2015
Review: I tend to evaluate books to a large extent on whether they’re suited to self-study or useful as a supplement. (If you have a course with a required text, you’ll have to get it, and reviews won’t matter much.) Cullen’s book is definitely useful for self-study … with some caveats.
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.
Name: gobberpooper
Rating: 4.0 out of 5 stars
Title: Engineer’s Advice: Be Patient
Date: Reviewed in the United States on July 20, 2017
Review: I got this book to brush up on my linear algebra. I’m looking to get into digital signal processing, and matrix operations are absolutely vital to pretty much everything a computer does. I approached this book as an engineer, meaning I just wanted a couple cheat sheets and quick algorithms to get out of it that I could then apply to a program, while chucking all the mathematical formality and notation out the window.
And because of that, by the second chapter I was failing miserably. I thought I could skim over the first chapter because I legitimately did know and remember all the concepts in it. I know matrix multiplication, I know what row reduced echelon form is, I know the basics of solving systems of equations with matrices etc. As I went on, I found myself unable to understand any of the book. And then I went back, and right there in chapter 1.1, it explains exactly what every little notation is. I had to get myself into a mathematical mindset. There’s all sorts of seemingly trivial little details, little caveats and exceptions and specific wording that’s actually crucial.
Trust me, if you use this book, you will understand every single little tiny detail of matrices so incredibly well. But! You have to work through it. Don’t skip anything. If some proof looks scary and complex, it’s because you skipped something earlier in the book. Sometimes it will go “And now from this equation we go to this equation” and some notation that you thought you knew what it meant but you really don’t, and you’ll wonder why he skipped like 10 steps. Then you go back and realize those 10 steps could all be condensed into one simple theorem explained a couple subchapters back. If you have to reread a proof 5 times to get it, do it. If all you know is arithmetic, algebra, and some basic calculus (high school math pretty much), you can become a master of matrices by the end of this book.
This book is for the patient, that is for sure. Stick with it and you’ll be amazed at how far you get.
Name: John M. Ford
Rating: 4.0 out of 5 stars
Title: Matrices Made Plain
Date: Reviewed in the United States on October 18, 2010
Review: 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,