Miniversal deformations of chains of linear mappings
T.N. Gaiduk, V.V. Sergeichuk, N.A. Zharko
TL;DR
This paper extends Arnold's concept of miniversal deformations from matrices to chains of linear mappings, providing a canonical form that smoothly parametrizes all nearby configurations.
Contribution
It introduces a miniversal deformation framework for chains of linear mappings, generalizing Arnold's results to more complex quiver representations.
Findings
Derived a miniversal deformation for chains of linear mappings
Unified deformation theory for matrix chains and quiver representations
Provided explicit canonical forms for nearby deformations
Abstract
V.I. Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to A, can be reduced by similarity transformations smoothly depending on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Elasticity and Wave Propagation · Advanced Theoretical and Applied Studies in Material Sciences and Geometry