F01QGF | $RQ$ factorization of real $m$ by $n$ upper trapezoidal matrix $\left(m\le n\right)$ |

F01QJF | $RQ$ factorization of real $m$ by $n$ matrix $\left(m\le n\right)$ |

F01QKF | Operations with orthogonal matrices, form rows of $Q$, after $RQ$ factorization by F01QJF |

F01RGF | $RQ$ factorization of complex $m$ by $n$ upper trapezoidal matrix $\left(m\le n\right)$ |

F01RJF | $RQ$ factorization of complex $m$ by $n$ matrix $\left(m\le n\right)$ |

F01RKF | Operations with unitary matrices, form rows of $Q$, after $RQ$ factorization by F01RJF |

F05AAF | Gram–Schmidt orthogonalization of $n$ vectors of order $m$ |

F06QPF | $QR$ factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix |

F06QQF | $QR$ factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row |

F06QRF | $QR$ or $RQ$ factorization by sequence of plane rotations, real upper Hessenberg matrix |

F06QSF | $QR$ or $RQ$ factorization by sequence of plane rotations, real upper spiked matrix |

F06QTF | $QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ real upper triangular, $P$ a sequence of plane rotations |

F06TPF | $QR$ factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix |

F06TQF | $QR$ factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row |

F06TRF | $QR$ or $RQ$ factorization by sequence of plane rotations, complex upper Hessenberg matrix |

F06TSF | $QR$ or $RQ$ factorization by sequence of plane rotations, complex upper spiked matrix |

F06TTF | $QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ complex upper triangular, $P$ a sequence of plane rotations |

F08AEF | $QR$ factorization of real general rectangular matrix |

F08AFF | Form all or part of orthogonal $Q$ from $QR$ factorization determined by F08AEF, F08BEF or F08BFF |

F08AGF | Apply orthogonal transformation determined by F08AEF, F08BEF or F08BFF |

F08AHF | $LQ$ factorization of real general rectangular matrix |

F08AJF | Form all or part of orthogonal $Q$ from $LQ$ factorization determined by F08AHF |

F08AKF | Apply orthogonal transformation determined by F08AHF |

F08ASF | $QR$ factorization of complex general rectangular matrix |

F08ATF | Form all or part of unitary $Q$ from $QR$ factorization determined by F08ASF, F08BSF or F08BTF |

F08AUF | Apply unitary transformation determined by F08ASF, F08BSF or F08BTF |

F08AVF | $LQ$ factorization of complex general rectangular matrix |

F08AWF | Form all or part of unitary $Q$ from $LQ$ factorization determined by F08AVF |

F08AXF | Apply unitary transformation determined by F08AVF |

F08BEF | $QR$ factorization of real general rectangular matrix with column pivoting |

F08BFF | $QR$ factorization of real general rectangular matrix with column pivoting, using BLAS-3 |

F08BHF | Reduces a real upper trapezoidal matrix to upper triangular form |

F08BKF | Apply orthogonal transformation determined by F08BHF |

F08BSF | $QR$ factorization of complex general rectangular matrix with column pivoting |

F08BTF | $QR$ factorization of complex general rectangular matrix with column pivoting, using BLAS-3 |

F08BVF | Reduces a complex upper trapezoidal matrix to upper triangular form |

F08BXF | Apply unitary transformation determined by F08BVF |

F08CEF | $QL$ factorization of real general rectangular matrix |

F08CFF | Form all or part of orthogonal $Q$ from $QL$ factorization determined by F08CEF |

F08CGF | Apply orthogonal transformation determined by F08CEF |

F08CHF | $RQ$ factorization of real general rectangular matrix |

F08CJF | Form all or part of orthogonal $Q$ from $RQ$ factorization determined by F08CHF |

F08CKF | Apply orthogonal transformation determined by F08CHF |

F08CSF | $QL$ factorization of complex general rectangular matrix |

F08CTF | Form all or part of orthogonal $Q$ from $QL$ factorization determined by F08CSF |

F08CUF | Apply unitary transformation determined by F08CSF |

F08CVF | $RQ$ factorization of complex general rectangular matrix |

F08CWF | Form all or part of orthogonal $Q$ from $RQ$ factorization determined by F08CVF |

F08CXF | Apply unitary transformation determined by F08CVF |

F08ZEF | Computes a generalized $QR$ factorization of a real matrix pair |

F08ZFF | Computes a generalized $RQ$ factorization of a real matrix pair |

F08ZSF | Computes a generalized $QR$ factorization of a complex matrix pair |

F08ZTF | Computes a generalized $RQ$ factorization of a complex matrix pair |

© The Numerical Algorithms Group Ltd, Oxford UK. 2013