Interpolative decomposition

In numerical analysis, interpolative decomposition (ID) factors a matrix as the product of two matrices, one of which contains selected columns from the original matrix, and the other of which has a subset of columns consisting of the identity matrix and all its values are no greater than 2 in absolute value.
Definition.
Let formula_1 be an formula_2 matrix of rank formula_3. The matrix formula_1 can be written as
where
Note that a similar decomposition can be done using the rows of formula_1 instead of its columns.
Example.
Let formula_1 be the formula_19 matrix of rank 2:
If
then 