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arXiv · 0709.2485

Canonical matrices for linear matrix problems

Vladimir V. Sergeichuk
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Abstract

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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BibTeXRIS

Vladimir V. Sergeichuk. 2007-09-16. Canonical matrices for linear matrix problems. https://doi.org/10.1016/s0024-3795(00)00150-6

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