Miniversal deformations of chains of linear mappings

Abstract

V.I. Arnold 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 depend- ing on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings V1 V2 · · · Vt , where all Vi are complex or real vector spaces and each line denotes