created 10/24/98; revised 08/01/00, 07/28/03

# CHAPTER 14 — Matrix times Column Matrix

A matrix and a column matrix can be multiplied together if their dimensions allow for it. This is a fundamental operation in modern computer graphics (and in many other applictions). It is so fundamental that it is implemented in silicon in all but the most crude of graphics cards. When a 3D graphics program is running the operation is performed millions of times per second.

#### Chapter Topics:

• Dimensions of the operands and of the result.
• Matrix-column matrix multiplication.
• row matrix-Matrix multiplication.
• How each element of the result is a dot product.

You have seen several multiplication-like operations before:

• Scalar times a scalar, resulting in a scalar.
• Scalar times a column matrix, resulting in a column matrix.
• Column matrix dot-product with a column matrix, resulting in a scalar.

### QUESTION 1: What type of object (do you suppose) is the result of a matrix times a column matrix?