Canonical form with respect to semiscalar equivalence for a matrix pencil with nonsingular first matrix

• Date: 2011
• Main Authors: Prokip, V. M., Прокіп, В. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2793
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Polynomial matrices $A(x)$ and $B(x)$ of size $n \times n$ over a field $\mathbb{F}$ are called semiscalar equivalent if there exist a nonsingular $n \times n$ matrix $P$ over $\mathbb{F}$ and an invertible $n \times n$ matrix $Q(x)$ over $\mathbb{F}[x]$ such that $A(x) = PB(x)Q(x)$. We give a canon...