  We present a uniform methodology for computing with finitely generated matrix
groups over any infinite field. As one application, we completely solve the
problem of deciding finiteness in this class of groups. We also present an
algorithm that, given such a finite group as input, in practice successfully
constructs an isomorphic copy over a finite field, and uses this copy to
investigate the group's structure. Implementations of our algorithms are
available in MAGMA.
