  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. In a recent paper, a new method was proposed that gives an answer to
that problem. In the present article conditions are given for the more general
problem of putting set of matrices into block-diagonal form simultaneously. In
addition, two algorithms for simultaneous block triangularization and block
diagonalization of sets of matrices are presented and are applied to several
concrete examples using the symbolic manipulation system Maple.
