On the equivalence of polynomial matrices over a field
UDC 512.64 The polynomial $(n\times n)$ matrices $A(\lambda )$ and $B(\lambda)$ over a field ${\mathbb F}$ are  called semiscalar equivalent if there exists a nonsingular $(n\times n)$ matrix $P$ over ${\mathbb F}$ and  an invertible $(n\times n)$  polynomial m...
Saved in:
| Date: | 2024 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7926 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 512.64
The polynomial $(n\times n)$ matrices $A(\lambda )$ and $B(\lambda)$ over a field ${\mathbb F}$ are  called semiscalar equivalent if there exists a nonsingular $(n\times n)$ matrix $P$ over ${\mathbb F}$ and  an invertible $(n\times n)$  polynomial matrix $Q(\lambda )$ over ${\mathbb F[\lambda}]$ such that $A(\lambda ) = PB(\lambda )Q(\lambda )$.  We establish conditions under which nonsingular polynomial matrices $A(\lambda )$ and $B(\lambda )$  are semiscalar equivalent.  As a consequence, we present the conditions of equivalence and similarity of two sets of $(n\times n)$  matrices over an arbitrary field ${\mathbb F}.$ |
|---|---|
| DOI: | 10.3842/umzh.v76i5.7926 |