# Structural stability of matrix pencils and of matrix pairs under contragredient equivalence

### Abstract

UDC 512.64A complex matrix pencil $A-\lambda B$ is called structurally stable if there exists its neighborhood in which all pencils are strictly equivalent to this pencil. We describe all complex matrix pencils that are structurally stable. It is shown that there are no pairs $(M,N)$ of $m\times n$ and $n\times m$ complex matrices ($m,n\ge 1$) that are structurally stable under the contragredient equivalence $(S^{-1}MR, R^{-1}NS),$ in which $S$ and $R$ are nonsingular.

Published

25.05.2019

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 71, no. 5, May 2019, pp. 706-9, https://umj.imath.kiev.ua/index.php/umj/article/view/1468.

Issue

Section

Short communications