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Philip N. Klein

Coding the Matrix: Linear Algebra through Applications to Computer Science 8.4.2013 Edition

by Philip N. Klein (Author)

4.5 165 ratings

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An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.

Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program

ISBN-10

0615880991
ISBN-13

978-0615880990
Edition

8.4.2013
Publication date

September 3, 2013
Language

English
Dimensions

8.5 x 1.24 x 11 inches
Print length

548 pages
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Editorial Reviews

About the Author

Philip Klein is Professor of Computer Science at Brown University. He was a recipient of the National Science Foundation's Presidential Young Investigator Award, and has received multiple research grants from the National Science Foundation. He has been made an ACM Fellow in recognition of his contributions to research on graph algorithms. He is a recipient of Brown University's Award for Excellence in Teaching in the Sciences. Klein received a B.A. in Applied Mathematics from Harvard and a Ph.D. in Computer Science from MIT. He has been a Visiting Scientist at Princeton's Computer Science Department, at MIT's Mathematics Department, and at MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL), where he is currently a Research Affiliate. Klein has worked at industry research labs, including Xerox PARC and AT&T Labs, and he has been Chief Scientist at three start-ups. Klein was born and raised in Berkeley, California. He started learning programming in 1974, and started attending meetings of the Homebrew Computer Club a couple of years later. His love for computer science has never abated, but in a chance encounter with E. W. Dijkstra in 1979, he was told that, if he wanted to do computer science, he had better learn some math. His favorite xkcd is 612.

Product details

Publisher ‏ : ‎ Newtonian Press; 8.4.2013 edition (September 3, 2013)
Language ‏ : ‎ English
Paperback ‏ : ‎ 548 pages
ISBN-10 ‏ : ‎ 0615880991
ISBN-13 ‏ : ‎ 978-0615880990
Item Weight ‏ : ‎ 2.77 pounds
Dimensions ‏ : ‎ 8.5 x 1.24 x 11 inches

Best Sellers Rank: #101,109 in Books (See Top 100 in Books)
- #6 in Computer Networks
- #8 in Mathematical Matrices
- #14 in Linear Algebra (Books)

Customer Reviews:
4.5 165 ratings

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A reviewer from Sydney Australia

Reviewed in the United States 🇺🇸 on October 9, 2015

Verified Purchase

I rarely write book reviews but I am compelled to write one for Coding the Matrix. This book first caught my attention when a course by the same name was offered at Coursera. I did not enroll in the course but instead bought the book for self study at some stage. This year, I spent 5 months working through the problems in the book (I am down to the last 2 of the 14 chapters) and I just want to say that I really wish there was a book like this in bookstores 20 years ago. What a fantastic way to teach Linear Algebra!! Previously, I had tried working through Gilbert Strang's book and video lectures on Linear Algebra but the material never stuck in my head. This book is quite different in its approach because it spends a lot of time providing the intuition behind fundamental concepts. What is the intuition behind a Matrix? What is the "meaning" of Matrix multiplication? What really is a Vector Space? What is the relationship between a Matrix and a Function? The author goes about explaining these basic concepts using a combination of worked exercises and hands on Python implementations. After working through this book I am convinced that implementing Linear Algebra algorithms and applying them to real world problems is the most effective way to learn the subject.

The hard copy book has several typos and errors but the Kindle version has been updated to fix most of these. Still, before you start, I suggest downloading the errata from the book's website just to be sure. The book has a short intro on Python which I thought was quite sufficient to tackle the programming exercises. This book requires real hard work if you want to get through it. Many times (especially in the Orthogonalization and Special Bases chapters) I found the going tough. But don't be discouraged - it is worth the effort. Now I really understand what QR factorization is about. SVD? No worries. The chapter on SVD starts with the absolute basics to explain how to derive the SVD formula and what the various component matrices really mean. I don't think I will ever see a A * A' multiplication in any other book without recollecting the beautiful explanation of orthonormal vectors from this book. The sad part for me is that I had to use all these concepts in the past working as a quant analyst at a bank, not knowing what these concepts really meant. So yeah, I wish it was published ages ago.

Thank you Prof Klein for writing this book. The teaching technique you have employed for such a complicated topic is unique and effective. Looking forward to the next edition.

59 people found this helpful

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Tamara

Great book

Reviewed in the United States 🇺🇸 on March 10, 2023

Verified Purchase

If you are a programmer and want to learn linear algebra, this is the way to do it. It is fun to work through because there are plenty of exercises and none of them are too hard.

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Customer_D

I'd like to give this 4

Reviewed in the United States 🇺🇸 on July 7, 2016

Verified Purchase

I'd like to give this 4.5 stars...

The author explains some really deep concepts extremely well. In particular Chapter 9 on Orthogonalization is extremely well done. I also thought the chapters on the SVD and Eigenvalues were quite well done. On top of this, there are also some unexpected bonuses like gradient decent and the discrete fourier transform.

My one major complaint is the author's choice of notation. Two things jump out: using zero based indexing at times and then switching back to counting starting with 1 at later times with the excuse that it is more common in math. The author is a CS prof, after all, and uses zero based indexing for Python -- the entire book should have used zero based indexing. (Dijkstra would approve.) Switching back and forth add complexity with no counterbalancing benefit.

More critically, I think the author's choice of treating a vector primarily as a 1 dimensional array (and thus as a flat python list) is a mistake. That interpretation should be a backup, and the primary should be that the vector is a column vector and hence has dimensions of n x 1, of 1 x n if it is transposed. This is a touch more work up front, but following dimensions is immensely useful in large math problems (and I would put this under the umbrella of dimensional analysis in general -- even though that tends to be oriented towards physical units for scalars).

All that said, I'd still give this 4.5 stars as there are some extremely good things in here. And for ~$30 it is considerably cheaper than most text books.

10 people found this helpful

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HJ

Too Self Referential

Reviewed in the United States 🇺🇸 on February 14, 2021

Verified Purchase

I've made some progress with this book, but I find it to be a bit unergonomic to use. You need to jump back in the book fairly often to find material that gets referenced later. The author also starts a problem and leaves a lot dangling to (maybe?) be addressed later in the book. This may be fine for some readers, but it is not a style I enjoy. For my purposes, I switched to a Mathematics for Machine Learning Coursera course and have rapidly made more progress.

One person found this helpful

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JWS

Very Good Intro to Linear Algebra

Reviewed in the United States 🇺🇸 on August 12, 2015

Verified Purchase

This book is takes a fairly unique approach to introducing linear algebra. Unlike a lot of linear algebra texts, it provides a large number of examples and applications using real world scenarios (error correcting codes, encryption, etc.) It is well written, with some humorous touches here and there. It uses Python to implement the algorithms, but these sections can easily be skipped if you just want to use the text as an intro to linear algebra.

Another plus is that the Kindle edition is a print facsimile, which means mathematical expressions are rendered properly and at a size that is easily readable. This is an aggravating problem with most Kindle books for technical subjects. The only downside is that there is no index.

There are a few curious errors: in one diagram the numeral 1 is consistently replaced by an exclamation point (!). In another diagram, the Greek letter theta is replaced in several spots by, again, an exclamation point. These issues do not, however, detract from the overall value of the book and I highly recommend it.

16 people found this helpful

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