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

Charles G. Cullen (Author)

Book Description

ISBN-10: 0486663280 | ISBN-13: 978-0486663289 | Publication Date: May 1, 1990 | Edition: 2nd

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.

Product Details

• 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: 4.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #35,367 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

33 of 33 people found the following review helpful:

5.0 out of 5 stars Supreme intro to advanced linear algebra and matrix analysis, July 14, 2003

By 

Sweetcheeks McMuffin (Ohio, USA) - See all my reviews

This review is from: Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) (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.

25 of 27 people found the following review helpful:

5.0 out of 5 stars Linear algebra is fun, December 3, 2003

By A Customer

This review is from: Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) (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.

20 of 22 people found the following review helpful:

5.0 out of 5 stars Advanced undergraduate reference, July 5, 2005

By 

Peter Kwok - See all my reviews
(REAL NAME)   

This review is from: Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics) (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.