Canonical matrices for linear matrix problems

Details Canonical matrices for linear matrix problems Canonical matrices for linear matrix problems

2007-09-16

arxiv.org/abs/0709.2485v1

Linear Algebra Appl. 317 (2000) 53-102

Mathematics

Representation Theory

59 pages

Scientific paper

10.1016/S0024-3795(00)00150-6

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).

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