  We consider a large class of matrix problems, which includes the problem of
classifying arbitrary systems of linear mappings. For every matrix problem from
this class, we construct Belitskii's algorithm for reducing a matrix to a
canonical form, which is the generalization of the Jordan normal form, and
study the set C(m,n) of indecomposable canonical m-by-n matrices. Considering
C(m,n) as a subset in the affine space of m-by-n matrices, we prove that either
C(m,n) consists of a finite number of points and straight lines for every
(m,n), or C(m,n) contains a 2-dimensional plane for a certain (m,n).
