Practical Linear Algebra
A Geometry Toolbox
, Second edition

by Gerald Farin & Dianne Hansford

published by A K Peters, Ltd. 2005
384 pages, ISBN: 1-56881-234-5

Third edition available 20 August 2013


After having finished your book today, I agree completely with the very favorable reviews that I saw on the internet. It was an enlightening experience to brush up my old university math with this book. The 'sketchy' way of explaining things sure worked for me.

Dr. Anneke Sicherer-Roetman, Maritime Research Institute Netherlands
August 2008

First of all, many thanks to you and Professor Hansford for creating "Practical Linear Algebra, A Geometry Toolbox," it's done a world of wonder for me, as I need to review my linear algebra to prepare for studying computer graphics. I really can't thank you enough.

Daniel Kurtz
College of Computer and Information Science, Northeastern University, Boston, MA, USA
April 2007

Your book "Pratical Linear Algebra, a geometry toolbook " is great. I write software for image analysis of medical images where in several occasions I have to deal with eigen things and similar . I have been using your book as a valuable reference to refresh and understand these concepts that I studied when I was a student.

Diego Bordegari
April 2006

I picked up this book with the thought, ’oh, another linear algebra text.’ I was pleasantly surprised, upon examination, that it is not just another one. The standard linear algebra material is presented with good motivating stories, illustrations and examples.

Review in its entirety.

Canadian Mathematical Society (CMS) Notes
February 2006

[The] mixture of linear algebra, geometry, and numerical aspects is very interesting and will probably stimulate the students.

Review in its entirety.

Bulletin of the Belgian Mathematical Society
December 2005

It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand.

Review in its entirety

Choice Magazine
September 2005

I just purchased your book, "Practical linear algebra", a few days ago. I found it in Barns and Nobles last week, and I immediately fell in love with it. I love the nice illustrations and diagrams which are very helpful in promoting intuitive understanding of every concept. I am a clinician investigator at the National Institutes of Health who is conducting MRI research of the heart. My main interest is finite deformation of the heart muscle structures, however, since I do not have engineering background, I have been looking for a nice textbook on linear algebra.

Hiroshi Ashikaga, MD
National Institute of Health
February 2005

I am taking a Linear Algebra class -- geez, what a frustrating experience. A paedagogical disaster. We are all non-math students -- but no applications, no substantive interpretations of any concept. And then, panicking for finals, I went to the Math library, found your book, and was delighted. I was awake last night til 4am, reading it just for pleasure. keep up the good work!

Juan Pablo Zuluaga
Pitt University
April 2005

Teaching computer graphics and mathematics in the study program Digital Media at Bremen, Germany, I have found "Practical Linear Algebra" to be precisely the kind of book I've long been looking for. It covers all topics that are vital for computer graphics, even gives lots of applications in that field including for instance PostScript, and does so in a very practical but nonetheless rigorous manner. I find many elements of my own teaching in this book, including the hand-made style of drawings (rendering them more "hands-on"), using a geometric shape to illustrate the action of a 2x2 matrix, and deriving the determinant from the computation of areas and volumes instead of plainly presenting a formula. I have recommended this book strongly to all students in my first-year courses and will continue to do so.

Prof. Dr. Jörn Loviscach
University of Applied Sciences
Fachbereich Elektrotechnik und Informatik
Hochschule Bremen, Germany
May 2005

I looked at the Practical Linear Algegra book and I was impressed with the applications, especially those related to computer graphics. The topics are organized in a slightly non-traditional way, so the book does not coordinate with our current course outline as easily as some other books do. However, I think some faculty will be interested in using the book because the geometric descriptions and applications are very nice.

Prof. Linda Patton
Mathematics Deparment
Cal Poly San Luis Obispo
December 2005

Is linear algebra a tool that is capable of solving a myriad of problems or an example of mathematical structures and reasoning? The answer, of course, is both. In this book, Farin and Hansford certainly take the first viewpoint. Common theorem-proof presentation has been replaced by motivation, example, or graphics. Their goal is aimed at the freshman/sophomore level and is quite appropriate for students in engineering and computer graphics as well as in mathematics. It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand. As a consequence, it is significantly different from a traditional work in the area. For example, "eigen things" (their term) are introduced in the plane and used to diagonalize a symmetric matrices, but the general problem of diagonalizing a matrix is omitted. There is no mention of similar matrices. It appears to be a very good book, if the goal is introduction to applicaiton, but perhaps not for introduction to mathematical proofs. Summing Up: Recommended. Lower-division undergraduates; two-year technical program students.

J.R. Burke
Gonzaga University

Published in CHOICE Current Reviews for Academic Libraries
September 2005, Vol. 43 No. 01
Science & Technology, Mathematics

We have been quite appreciative of the reviews and feedback from readers of the first edition of this text, The Geometry Toolbox. Reviews are included below.

Written in a deceptively easy-to-read style, ... this textbook provides a solid foundation in the mathematics needed for graphics and modeling. ....
The clarity of the style and the geometric nature of each explanation by themselves makes this text an important reference. ...

--P. Samella
in Computing Reviews September 1998, pp 464-5

I am writing an intro computer science text and am reading all the other basic texts. Your new geometry toolbox book is TERRIFIC.

--Peter Shirley
School of Computing
University of Utah
email correspondence

This book has a number of important advantages. First, the book provides intuition into the vector meaning of transformations and manipulations. Furthermore, ...

--A. Fischer
Dept. of Mechanical Eng.
CMSR Lab. for Computer Graphics and CAD
Technion- Israel Inst. of Technology
in Computer Aided Design
vol 32, issue 4, 2000

Your book, The Geometry Toolbox, is without a doubt one of the best written pedagogical works I've ever read and certainly the best in geometry.

--Lewis Stiller
email correspondence

...I am working on a Masters of Computer Science at Syracuse University. I also work at Lockheed Martin on a trainer/simulator for a sonar system ....

I found your book at the SU math library. Is excellent. Part of my job involves contact geometry and I have found your book to be helpful. I like the fact that it is done in postscript. Some of the best looking books ever are done in postscript. ....

On my own time, I am a 2D/3D hobbiest. I have various books on OpenGL and Java graphics programming and VRML. Your book will come in handy for this also.

--David Danner
email corresponance

American Mathematical Monthly, Feb. 1999.
Mathematical Reviews, Issue 99d.
Johannes Wallner. Zentralblatt fuer Mathematik, issue 899, 1999.