OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 4.3, Eighth Edition

Matrix Multiply Refresher

For our use, matrices and matrix multiplication are nothing more than a convenient mechanism for expressing linear transformations, which in turn are a useful way to do the coordinate manipulations needed for displaying models. The vital matrix mechanism is explained here, while interesting uses for it will come up in numerous places in subsequent discussions.

First, a definition. A 4 × 4 matrix takes a four-component vector to another four-component vector through multiplication by the following rule:

Now, some observations.

• Each component of the new vector is a linear function of all the components of the old vector, ...