2000/09/01 by Vladimir V. Sergeichuk · 4 citations
Computer Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Matrix Theory and Algorithms #math.RT #msc:15A21 #msc:16G60
paper · pdf · doi:10.1016/s0024-3795(00)00150-6
published as Linear Algebra Appl. 317 (2000) 53-102 · 59 pages
openalex publication_date 2000/09/01 · arxiv created 2007/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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).