created 10/24/98; revised 08/01/00, 07/28/03, 07/25/09, 03/09/15

A matrix and a column matrix can be multiplied together if their dimensions allow for it. This is a fundamental operation in computer graphics (and in many other fields). When a 3D graphics program is running the operation is performed millions of times per second.

- 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

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