# Keyword : Orthogonal

 f08afc Form all or part of orthogonal $Q$ from $QR$ factorization determined by f08aec, f08bec or f08bfc f08agc Apply orthogonal transformation determined by f08aec, f08bec or f08bfc f08ajc Form all or part of orthogonal $Q$ from $LQ$ factorization determined by f08ahc f08akc Apply orthogonal transformation determined by f08ahc f08bhc Reduces a real upper trapezoidal matrix to upper triangular form f08bkc Apply orthogonal transformation determined by f08bhc f08cfc Form all or part of orthogonal $Q$ from $QL$ factorization determined by f08cec f08cgc Apply orthogonal transformation determined by f08cec f08cjc Form all or part of orthogonal $Q$ from $RQ$ factorization determined by f08chc f08ckc Apply orthogonal transformation determined by f08chc f08fec Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form f08ffc Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec f08fgc Apply orthogonal transformation determined by f08fec f08gec Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage f08gfc Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec f08ggc Apply orthogonal transformation determined by f08gec f08hec Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form f08kec Orthogonal reduction of real general rectangular matrix to bidiagonal form f08kfc Generate orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec f08kgc Apply orthogonal transformations from reduction to bidiagonal form determined by f08kec f08nec Orthogonal reduction of real general matrix to upper Hessenberg form f08nfc Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec f08ngc Apply orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec f08qfc Reorder Schur factorization of real matrix using orthogonal similarity transformation f08vec Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair f08vsc Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair f08wec Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form f08yfc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation f08ygc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces g04eac Computes orthogonal polynomials or dummy variables for factor/classification variable g05pxc Generates a random orthogonal matrix

© The Numerical Algorithms Group Ltd, Oxford UK. 2012