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

  • V. M. Prokip Iн-т прикл. пробл. механiки i математики НАН України, Львiв


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 canonical form with respect to the semiscalar equivalence for a matrix pencil $A(x) = A_0x - A_1$, where $A_0$ and $A_1$ are $n \times n$ matrices over $\mathbb{F}$, and $A_0$ is nonsingular.
How to Cite
Prokip, V. M. “Canonical Form With Respect to Semiscalar Equivalence for a Matrix Pencil With Nonsingular First Matrix”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 8, Aug. 2011, pp. 1147-52,
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