f08aa solves linear least squares problems of the form where $A$ is an $m$ by $n$ real matrix of full rank, using a $QR$ or $LQ$ factorization of $A$.

f08ag multiplies an arbitrary real matrix $C$ by the real orthogonal matrix $Q$ from a $QR$ factorization computed by (F08AEF not in this release) f08be f08bf.

f08an solves linear least squares problems of the form where $A$ is an $m$ by $n$ complex matrix of full rank, using a $QR$ or $LQ$ factorization of $A$.

f08be computes the $QR$ factorization, with column pivoting, of a real $m$ by $n$ matrix.

f08bf computes the $QR$ factorization, with column pivoting, of a real $m$ by $n$ matrix.

f08fa computes all the eigenvalues and, optionally, all the eigenvectors of a real $n$ by $n$ symmetric matrix $A$.

f08fb computes selected eigenvalues and, optionally, eigenvectors of a real $n$ by $n$ symmetric matrix $A$. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

f08fl computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian $m$ by $m$ matrix $A$, or for the left or right singular vectors of a general $m$ by $n$ matrix $A$.

f08fp computes selected eigenvalues and, optionally, eigenvectors of a complex $n$ by $n$ Hermitian matrix $A$. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

f08kb computes the singular value decomposition (SVD) of a real $m$ by $n$ matrix $A$, optionally computing the left and/or right singular vectors.

f08kp computes the singular value decomposition (SVD) of a complex $m$ by $n$ matrix $A$, optionally computing the left and/or right singular vectors.

f08nb computes the eigenvalues and, optionally, the left and/or right eigenvectors for an $n$ by $n$ real nonsymmetric matrix $A$.

Optionally, it also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors, reciprocal condition numbers for the eigenvalues, and reciprocal condition numbers for the right eigenvectors.

f08np computes the eigenvalues and, optionally, the left and/or right eigenvectors for an $n$ by $n$ complex nonsymmetric matrix $A$.

Optionally, it also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors, reciprocal condition numbers for the eigenvalues, and reciprocal condition numbers for the right eigenvectors.

f08wb computes for a pair of $n$ by $n$ real nonsymmetric matrices $\left(A,B\right)$ the generalized eigenvalues and, optionally, the left and/or right generalized eigenvectors using the $QZ$ algorithm.

Optionally it also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors, reciprocal condition numbers for the eigenvalues, and reciprocal condition numbers for the right eigenvectors.

f08wp computes for a pair of $n$ by $n$ complex nonsymmetric matrices $\left(A,B\right)$ the generalized eigenvalues and, optionally, the left and/or right generalized eigenvectors using the $QZ$ algorithm.

Optionally it also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors, reciprocal condition numbers for the eigenvalues, and reciprocal condition numbers for the right eigenvectors.