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

Abstract

UDC 512.64
A 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.