The number of rows == the number of columns
In a square matrix the number of rows equals the number of columns. In computer graphics, square matrices are used for transformations.
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. At left is a 4 x 1 column matrix. A row matrix consists of a single row. (Some books use row matrices to represent geometical 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 (a directed line segment). In these notes, column matrices will be used to represent vectors and will also be used to represent geometric points.