  In an earlier paper, we showed that a large class of fast recursive matrix
multiplication algorithms is stable in a normwise sense, and that in fact if
multiplication of $n$-by-$n$ matrices can be done by any algorithm in
$O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done
stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend
this result to show that essentially all standard linear algebra operations,
including LU decomposition, QR decomposition, linear equation solving, matrix
inversion, solving least squares problems, (generalized) eigenvalue problems
and the singular value decomposition can also be done stably (in a normwise
sense) in $O(n^{\omega + \eta})$ operations.
