TY - JOUR
AU - M. I. García-Planas
AU - T. Klymchuk
PY - 2019/05/25
Y2 - 2024/10/13
TI - Structural stability of matrix pencils and of matrix pairs
under contragredient equivalence
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 5
SE - Short communications
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1468
AB - 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.
ER -