Canonical matrices for linear matrix problems
arXiv:0709.2485 · doi:10.1016/S0024-3795(00)00150-6
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).
59 pages
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Cited by in corpus (7)
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- Complexity of matrix problems
- Computation of the canonical form for the matrices of chains and cycles of linear mappings
- Canonical matrices of isometric operators on indefinite inner product spaces
- Estimate of the number of one-parameter families of modules over a tame algebra
- Rigid systems of second-order linear differential equations
- Miniversal deformations of chains of linear mappings