Game Physics Cookbook

Chapter 2. Matrices

In this chapter, we will cover the basic math needed to multiply and invert matrices:

• Definition
• Transpose
• Multiplication
• Identity matrix
• Determinant of a 2x2 matrix
• Matrix of minors
• Matrix of cofactors
• Determinant of a 3x3 matrix
• Operations of a 4x4 matrix
• Adjugate matrix
• Matrix inverse

Introduction

Matrices in games are used extensively. In the context of physics, matrices are used to represent different coordinate spaces. In games, we often combine coordinate spaces; this is done through matrix multiplication. In game physics, it's useful to move one object into the coordinate space of another object; this requires matrices to be inverted. In order to invert a matrix, we have to find its minor, determinant, cofactor, and adjugate. This ...