revised 08/01/00, 07/28/03, 07/20/05, 07/26/09, 03/10/15

This chapter discusses the product of two matrices. This is an extension of the ideas of the previous chapter.

- When matrices can be multiplied together
- Result is a matrix
- Each element of the result is a dot product
- Associative property
- Not commutative
- Distributive over addition
- Multiplication with the zero matrix

Matrix-matrix products are used in computer graphics to create the transformation matrices that operate on points and vectors. In a "first person game" such as DOOM the landscape is modeled with points and vectors. The constantly changing view you see as the hero moves through the landscape is created by transforming those points and vectors.

Do you think it possible to multiply the following two matrices?
**A**_{4×3} **B**_{3×5}

(Make a guess, based on what you know about multiplying a matrix with a column matrix.)