Linear Algebra for Computer Science
Abstract
This book has its origin in my experience teaching Linear Algebra to Computer Science students at Singapore Management University. Traditionally, Linear Algebra is taught as a pure mathematics course, almost as an afterthought, not fully integrated with any other applied curriculum. It certainly was taught that way to me. The course I was teaching, however, had a definite pedagogical objective of bringing out the applicability and the usefulness of Linear Algebra in Computer Science, which is nothing but applied mathematics. In today’s age of machine learning and artificial intelligence, Linear Algebra is the branch of mathematics that holds the most relevance to computing.One question I got from one of my brighter students the first time I taught the course was why they were forced to learn this particular branch of mathematics. It was not a defiant or rebellious question, but one of pure curiosity. I did not have a ready answer then, but I think I have one now. When we embark on any profession, we have to start with the tools of the trade. For instance, if we want to be a musician, we have to learn the notes before we can perform. If we want to be a writer, we need to know the words and the grammar of our chosen language first. Similarly, in order to be a computer scientist, we have to have the necessary mathematical skills. And Linear Algebra is arguably the most critical of the expertise needed, especially when it comes to dealing with large quantities of data efficiently.Linear Algebra is a well-established field, and we can find several resources freely available on the Internet. In writing this book, I have made use of many of them. In fact, the whole process of writing can be thought of as an exercise in curating the right pieces of information at the right level, and standardizing them with consistent notations to form a coherent and fluid narrative.Books on mathematics tend to be dry and often unreadable collec- tions of facts, theorems, proofs and problems. This type of discourse is understandable, given the nature of the subject that demands ac- curacy and completeness, often at the expense of readability. My objective was to write a book that would be read. For this reason, I set practicality as my goal, and even used, dare I say this, humor to keep my reader engaged.I employed two more tricks to improve the readability. The first one is to restrict the field (over which our vectors and matrices are defined) to real numbers (R) because of its relevance to computer science. The second trick is to pepper the text with “boxes,” which are curious and interesting applications, background info or other tidbits that are topic-adjacent to the subject matter under discussion.From experience, I know that a book of this length takes about a year to write and another year to polish and publish. The first version of this book was done and dusted in about three months, almost ten times faster than normal. For this reason, it is continuously updated, corrected and improved upon over the last couple of years. How my students respond to the course on which the book is based will also inspire further revisions. These new versions and/or editions are made available periodically.