Practical Linear Algebra: A Geometry Toolbox, Third Edition

by Gerald Farin, Dianne Hansford

Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.

New to the Third Edition



More exercises and applications Coverage of singular value decomposition and its application to the pseudoinverse, principal components analysis, and image compression More attention to eigen-analysis, including eigenfunctions and the Google matrix Greater emphasis on orthogonal projections and matrix decompositions, which are tied to repeated themes such as the concept of least squares

To help students better visualize and understand the material, the authors introduce the fundamental concepts of linear algebra first in a two-dimensional setting and then revisit these concepts and others in a three-dimensional setting. They also discuss higher dimensions in various real-life applications. Triangles, polygons, conics, and curves are introduced as central applications of linear algebra.

Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts. The authors website also offers the illustrations for download and includes Mathematica(r) code and other ancillary materials."

Genres: Mathematics, Textbooks

514 pages, Hardcover

First published December 15, 2004

Reviews

[Farsan Rashid · Rating 5 out of 5]

The first time I learned about geometric interpretation of Linear Algebra was from famous Youtube channel 3blue1brown, it was opening of a new horizon. After that I decided to read a book to be 'formally' introduced with major concepts in LA and learn about topics that are frequently mentioned in Machine learning (eigen, SVD, PCA etc). I tried Gilbert Strang but found it too dry so decided to find books that describes LA in the light of geometry and also covers all the keywords I had in mind. This book fitted in every aspect. I don't know whether I would have equally enjoyed or so easily grasped the concepts if I had not watched the 3blue1brown videos but also I do not find a single scope where the author could have done better. Every single topic (vector, matrix, inverse, shear, rotation, eigen, Gram-Schmidt, SVD, PCA etc...) is wonderfully explained both in 2D and 3D setting, also some dedicated chapters to discuss about higher dimensions.

The book website (http://www.farinhansford.com/books/pl...) contains lecture slides, images used in the book, Mathemetica scripts(to generate image), solution to exercises (for instructors). I suggest to take a look at the book if someone is teaching undergraduate LA.

The book also has lots of real life examples, almost all of them are related to graphics but also has some interesting examples like Google page rank matrix.

IMO title of this book is misleading and should have been something like "Geometric Interpretation of Linear Algebra".

My respect to the departed soul of author Gerald Farin who passed away on 14 January 2016 for this amazing book.

[Hilary Chang · Rating 5 out of 5]

This book uses a lot of pictures to show you how linear algebra applies in geometry and explains it in plain language. I'm never a fan of mathematics; but I find reading it enjoyable. I highly recommend this book to anyone who has done linear algebra but doesn't know what's the point of learning it, or who just wants to have some puzzles after a busy day.

[Charles · Rating 5 out of 5]

Linear algebra has traditionally been the class in the undergraduate math curriculum where the student makes the transition from "plug - n - chug" formula popping to mathematical proofs. However, in recent years linear algebra has taken on a new role, namely as the best class where applied mathematics can be visually demonstrated. The enormous advances in animated imagery have led to movies where the characters are a virtual hybrid of animated and real. I once taught a course in computer graphics for computer programmers and they were impressed when they applied a basic matrix multiplication to a figure and could watch the altered figure appear on the screen, albeit slowly. Quite frankly, they loved the course.
This book covers linear algebra before the appearance of formal proofs; I cannot recall seeing a single proof. That coverage is excellent and is focused on how images are created and modified using linear algebra. It is clearly written and illustrated and a tutorial on PostScript appears in an appendix. There is a set of exercises at the end of each chapter and the solutions to many of them are included.
A textbook for the modern use of linear algebra as an image creation and modification tool, it is ideal for any math program that wants to cover that material. In my experience, it would be a very popular course, but it cannot be used for any coverage of linear algebra that involves proofs.

Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon

[Bengt · Rating 5 out of 5]

Best book on linear algebra I have read.
The examples are clear and concise, and the content is easy to digest.

[Jia Chen · Rating 5 out of 5]

Wonderful book for people who study computer graphics.