An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the

QR factorization In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix ''A'' into a product ''A'' = ''QR'' of an orthogonal matrix ''Q'' and an upper triangular matrix ''R''. QR decom ...

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 factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is re ...

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