Coding the Matrix: Linear Algebra through Computer Science Applications

Written for readers who already know how to program, this text teaches the mathematics of vectors and matrices along with the algorithms that work on them. Each mathematical idea is introduced through a practical problem from computer science, and readers reinforce it by writing code that carries out the calculations and explores these applications.

The examples range widely, including error-correcting codes, geometric transformations used in graphics, face detection, encryption and secret sharing, factoring integers, correcting the perspective in a photograph, PageRank (the ranking method behind Google's search), and identifying cancer from measurements of cells.

The thirteen chapters move from functions and fields through vectors, vector spaces, matrices, bases and dimension, Gaussian elimination, inner products, special bases, the singular value decomposition, eigenvectors, and linear programs. A companion website, codingthematrix.com, supplies data and support code, and most assignments are graded automatically online. The book includes over two hundred illustrations, among them a selection of xkcd comics.