The column (or row) rank of a rectangular matrix of values (e.g., a sums of squares and cross-products matrix) is equal to the number of linearly independent columns (or rows) of elements in the matrix. If there are no columns that are linearly dependent on other columns, then the rank of the matrix is equal to the number of its columns and the matrix is said to have full (column) rank. If the rank is less than the number of columns, the matrix is said to have reduced (column) rank and is singular.

See also: matrix singularity.