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The number of rows == the number of columns

Square Matrix

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

square matrix

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.

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?