Customer Reviews

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

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4 star:		(1)
3 star:		(0)
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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.

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.

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.

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.

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.

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.