This is a tutorial on *vector*
algebra and *matrix* algebra from the viewpoint of computer graphics.
It covers most vector and matrix topics needed to read college-level computer
graphics text books. Most graphics texts cover these subjects in an appendix,
but it is often too short. This tutorial covers the same material at greater
length, and with many examples.

- Chapter 0 Points and Lines
- Chapter 1 Vectors, Points, and Column Matrices
- Chapter 2 Column Matrix Addition
- Chapter 3 Vector Addition
- Chapter 4 Vector Length
- Chapter 5 Vector Direction
- Chapter 6 Scaling and Unit Vectors
- Chapter 7 The Dot Product
- Chapter 8 Length and the Dot Product
- Chapter 9 The Angle between Two Vectors
- Chapter 10 The Angle between 3D Vectors
- Chapter 11 Projecting one Vector onto Another
- Chapter 12 Vector Cross Product
- Chapter 13 Matrices and Simple Matrix Operations
- Chapter 14 Matrix-Column Matrix Multiplication
- Chapter 15 Matrix-Matrix Multiplication
- Chapter 16 Identity Matrix and Matrix Inverse
- Index

Computer graphics requires more math than is covered here. The purpose of these notes is to expand on the mathematical appendix included with most graphics books, not to teach the mathematical material in the main text of those books.

Although primarily aimed at university computer science students, this tutorial is useful to any programmer interested in 3D computer graphics or 3D computer game programming. In spite of their appealing blood-and-gore covers, mass trade books on game programming require the same understanding of vectors and matrices as college text books (and usually defer these topics to the same skimpy mathematical appendix).

This tutorial is useful for more than computer graphics. Vectors and matrices are used in all scientific and engineering fields, and any other field that uses computers (are there any that don't?) In many fields, the vocabulary used for vectors and matrices does not match that used in computer graphics. But the ideas are the same, and reading these notes will take only a slight mental adjustment.

These notes assume that
you have studied plane geometry and trigonometry sometime in the past. Notions
such as *point*, *line*, *plane*, and *angle* should
be familiar to you. Other notions such as *sine*, *cosine*, *determinant*,*
real number*, and the common trig identities should at least be a distant
memory.

These pages were designed at 800 by 600 resolution. They have been (somewhat) tested with not-too-old versions of Firefox and Internet Explorer. Many pages require JavaScript, and some pages require Java. If you lack these (or are behind a firewall that blocks these) you will be able to read most pages, but the interactive features will be lost.

The zip file contains all the above instructional material as of July 26, 2009. Permission is granted to download it for personal use or for use in an educational institution.

Vector Lessons zip file 1,476,720 bytes

A mirror site that contains this material is: Mirror Site