An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine the rank of a matrix. The

singular value decomposition In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rota ...

can be used to generate an RRQR, but it is not an efficient method to do so. An RRQR implementation is available in MATLAB.

References

Matrix decompositions Numerical linear algebra {{Algorithm-stub