Matrices and Linear Transformations

by Charles G. Cullen

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.

Genres: Mathematics, Nonfiction

336 pages, Paperback

First published December 1, 1972

Reviews

[Erickson · Rating 3 out of 5]

The presentation is unclear for two reasons: firstly, while it is commendable that the author explicitly shows how the computation of matrices, including the large ones, can be done using several introduced concepts, it automatically causes the whole expression to be both cumbersome, messy and difficult to read. Secondly, the author uses unconventional notations such as Crd(x) for coordinate matrix of colume matrix x with respect to some basis and Mtx as matrix; while it is merely symbols, the accessibility is hampered to some extent because many other books do agree on some standard notations.

The book does cover some ideas not quite covered in other similar books, such as matrix analysis. And it is great that the author attempted in most cases to show how explicit computation can be done whenever new ideas are introduced, something many books are probably lacking. Therefore, for those who can ignore style and simply take in the content and brute-force calculations as it is, the book is good. For those who wishes to emphasize on elegance of method and presentation, I would not recommend the book. There ought to be more pleasant ones when it comes to presentation, such as Axler's Linear Algebra Done Right or Hoffmann-Kunze's Linear Algebra. Even Gilbert Strang's text on linear algebra is not quite as messy, in my opinion.

[Nick Black · Rating 4 out of 5]

Let's face it: to get anywhere or be anybody in this life, you have to have linear operations in the same part of your brain that recognizes your mother's face or makes you irritable when you forget to eat; you have to juggle matrices with the same swift deftness with which one moves first the left foot, and then the other. There's pitiable losers and there's totally k-rad winners; there's people who get degrees in something called "social science" and there's people who viscerally grok determinants and nilpotents and bases and these last, my droogies, are those who keep the world running, the dreamers of electric dreams. If you can't do it in a finite space, do it in an infinite space, and if you can't do it in an infinite vector space you very likely can't do it at all.

But I digress.

A solid set of problems, and everything I've ever learned about linear algebra (a field remarkable for the absolute crappiness of its texts, and the variety of that crappiness -- within sight at this moment lurk no less than three "Foo Linear Algebra" texts, all of them in their 4th edition at minimum, and all of them terrible trash). Admittedly, it's wearying.

[Darin]

Unlike Elementary Matrix Theory, by Howard Eves, this book does share a lot of material with the linear algebra texts published in 2010. However, there is still some material in this book, such as canonical forms, that doesn't typically appear in introductory linear algebra books. While the author does write clearly, the writing is at a more mathematically sophisticated level than the books aimed at introducing linear algebra to students in 2010. Considering the very cheap price of this Dover reprint, this is a worthwhile second book to have on linear algebra. See also Elementary Matrix Theory, by Howard Eves, to find a book with much material that is difficult to find in more recently published books.

[Lecea · Rating 3 out of 5]

A classic textbook that needs updated notations and proofs.