By default, the function returns a vector of three nested matrices, P, Q, and R, such that M . P = Q . R. Matrix P represents the pivoting matrix, matrix Q represents the orthogonal matrix, and matrix R represents the upper triangular matrix.

If pivoting is disabled, the function returns a vector of two nested matrices, Q and R, such that M = Q . R.

When pivoting is disabled, the nested matrices Q and R have equal dimensions, but different element values, when compared to their default counterparts.