HEADER

Function: _header_linear_algebra
Class: header
Section: linear_algebra
Doc:
 \section{Vectors, matrices, linear algebra and sets}
 \label{se:linear_algebra}

 Note that most linear algebra functions operating on subspaces defined by
 generating sets (such as \tet{mathnf}, \tet{qflll}, etc.) take matrices as
 arguments. As usual, the generating vectors are taken to be the
 \emph{columns} of the given matrix.

 Since PARI does not have a strong typing system, scalars live in
 unspecified commutative base rings. It is very difficult to write
 robust linear algebra routines in such a general setting. We thus
 assume that the base ring is a domain and work over its field of
 fractions. If the base ring is \emph{not} a domain, one gets an error as soon
 as a nonzero pivot turns out to be noninvertible. Some functions,
 e.g.~\kbd{mathnf} or \kbd{mathnfmod}, specifically assume that the base ring is
 $\Z$.