Miniversal deformations of observable marked matrices

Abstract

Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute miniversal deformations of a given pair when it is observable, and the subspace $\mathbb C^d\times\{0\}$ is marked. Moreover, we obtain the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation parameter. Copyright © 2013 JohnWiley & Sons, Ltd.