Guide to Computational Linear Algebra

[jemidiah]

0.1 Introduction

I decided to write this guide in the spirit of VBAhack's Cubic Spline Tutorial. Overall it attempts to be a self-contained (where possible) guide for implementing basic operations in linear algebra. Part 1 is an introduction to vectors and matrices. It can be skipped, but only if you're good at pattern matching or have done some linear algebra before. Part 2 covers the basic uses of linear algebra with an eye towards computer graphics. This guide is generally meant to be used in pieces--for instance, 2.3 and 1.5 together tell you how to rotate points in 2D using matrix multiplication. It would likely be too much information to read straight through if you are completely unfamiliar with linear algebra, though anyone interested is welcome to try.

This guide is meant to be different things to different people. It's meant to be a conceptual introduction to vectors and matrices, with many of the details left out for other sources to fill in. It's meant to be a search result when you search the forums for, say, "dot products", where you'll get a formula for computing dot products as well as an explanation of what they are.

This guide tries to assume very little about your mathematical background. You should be familiar with basic algebra--addition, multiplication, and so on, using symbols. Aside from that, your background is much less important than your ability to reason and deal with some symbolic notation, since (if you're reading this) the ideas should be (largely) new anyway. Enjoy!


0.2 Table of Contents

PART 1: Background and Definitions

1. What is Linear Algebra?
2. From Numbers to Vectors
3. Basic Algebra with Vectors
4. From Vectors to Matrices
5. Basic Algebra with Matrices

PART 2: Basic Computer Graphics with Linear Algebra

1. Dot Products
2. Cross Products
3. 2D Rotation Matrix
4. 3D Rotation Matrices