Canonical matrices for linear matrix problems Original Research Article

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 Belitskiimageʹs algorithm for reducing a matrix to a canonical form, which is the generalization of the Jordan normal form, and study the set Cmn of indecomposable canonical m×n matrices. Considering Cmn as a subset in the affine space of m×n matrices, we prove that either Cmn consists of a finite number of points and straight lines for every m×n, or Cmn contains a 2-dimensional plane for a certain m×n.