The number of rows == the number of columns

A **square matrix** has the same number of rows as columns.
In computer graphics,
square matrices are used for transformations.

A **rectangular matrix** is one where
the number of rows or columns may not be the same.
(Some books require that the number of rows and number of columns be different.)

A **column matrix** consists of a single column.
It is a N x 1 matrix.
These notes, and most computer graphics texts, use
column matrices to represent geometrical
vectors.
Below is a 4 x 1 column matrix.

A **row matrix**
consists of a single row.
(Some books use row matrices to represent
geometrical vectors).

Some books call a column matrix a
*column vector* and call a row matrix
a *row vector*.
This is OK, but can be ambiguous.
In these notes
the word *vector* will be used for
a geometric object.
In these notes,
column matrices will be used to represent
vectors and will also be used to represent
geometric points.

What are square matrices used for?