  A problem that is frequently encountered in a variety of mathematical
contexts, is to find the common invariant subspaces of a single, or set of
matrices. A new method is proposed that gives a definitive answer to this
problem. The key idea consists of finding common eigenvectors for exterior
powers of the matrices concerned. A convenient formulation of the Pl\"ucker
relations is then used to ensure that these eigenvectors actually correspond to
subspaces or provide the initial constraints for eigenvectors involving
parameters. A procedure for computing the divisors of totally decomposable
vector is also provided. Several examples are given for which the calculations
are too tedious to do by hand and are performed by coding the conditions found
into Maple.
