Buchumschlag

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2024
Hauptverfasser: Prokip , V., Прокіп, Володимир
Format: Artikel
Sprache:Ukrainisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2024
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/7926
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
Завантажити файл: Pdf

Institution

Ukrains’kyi Matematychnyi Zhurnal
_version_ 1860512818265063424
author Prokip , V.
Прокіп, Володимир
author_facet Prokip , V.
Прокіп, Володимир
author_sort Prokip , V.
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2024-11-22T08:15:25Z
description 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_str_mv 10.3842/umzh.v76i5.7926
first_indexed 2026-03-24T03:34:50Z
format Article
fulltext Skip to main content Skip to main navigation menu Skip to site footer Open Menu Ukrains’kyi Matematychnyi Zhurnal Current Archives Submissions Major topics of interest About About Journal Editorial Team Ethics & Disclosures Contacts Search Register Login Home / Login Login Required fields are marked with an asterisk: * Subscription required to access item. To verify subscription, log in to journal. Login Username or Email * Required Password * Required Forgot your password? Keep me logged in Login Register Language English Українська Information For Readers For Authors For Librarians subscribe Subscribe Latest publications Make a Submission Make a Submission STM88 menghadirkan Link Gacor dengan RTP tinggi untuk peluang menang yang lebih sering! Bergabunglah sekarang dan buktikan keberuntungan Anda! Pilih STM88 sebagai agen toto terpercaya Anda dan nikmati kenyamanan bermain dengan sistem betting cepat, result resmi, dan bonus cashback harian.
id umjimathkievua-article-7926
institution Ukrains’kyi Matematychnyi Zhurnal
keywords_txt_mv keywords
language Ukrainian
last_indexed 2026-03-24T03:34:50Z
publishDate 2024
publisher Institute of Mathematics, NAS of Ukraine
record_format ojs
resource_txt_mv umjimathkievua/71/d31d9ddaae1acac5bebd4f383e6b8071
spelling umjimathkievua-article-79262024-11-22T08:15:25Z On the equivalence of polynomial matrices over a field Про еквівалентність многочленних матриць над полем Prokip , V. Прокіп, Володимир polynomial matrix, equivalence of matrices, semi-scalar equivalence of matrices , similarity of sets of matrices Еквівалентність матриць 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 ${\mathbb F}.$ УДК 512.64 Кажуть, що многочленні $(n\times n)$-матриці $A(\lambda )$ і $B(\lambda )$ над полем ${\mathbb F}$  напівскалярно еквівалентні, якщо існують неособлива матриця $P$ над ${\mathbb F}$ та зворотна многочленна $(n\times n)$-матриця $Q(\lambda )$ над ${\mathbb F[\lambda}]$ такі, що  $A(\lambda )=PB(\lambda )Q(\lambda ).$ Встановлено умови, за яких неособливі многочленні матриці $A(\lambda )$ і $B(\lambda )$ напівскалярно еквівалентні. Як наслідок, наведено умови еквівалентності та подібності двох наборів $(n\times n)$-матриць над довільним полем ${\mathbb F}.$  Institute of Mathematics, NAS of Ukraine 2024-06-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7926 10.3842/umzh.v76i5.7926 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 5 (2024); 743 - 750 Український математичний журнал; Том 76 № 5 (2024); 743 - 750 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/7926/9944 Copyright (c) 2024 Володимир Михайлович Прокіп
spellingShingle Prokip , V.
Прокіп, Володимир
On the equivalence of polynomial matrices over a field
title On the equivalence of polynomial matrices over a field
title_alt Про еквівалентність многочленних матриць над полем
title_full On the equivalence of polynomial matrices over a field
title_fullStr On the equivalence of polynomial matrices over a field
title_full_unstemmed On the equivalence of polynomial matrices over a field
title_short On the equivalence of polynomial matrices over a field
title_sort on the equivalence of polynomial matrices over a field
topic_facet polynomial matrix
equivalence of matrices
semi-scalar equivalence of matrices
similarity of sets of matrices
Еквівалентність матриць
url https://umj.imath.kiev.ua/index.php/umj/article/view/7926
work_keys_str_mv AT prokipv ontheequivalenceofpolynomialmatricesoverafield
AT prokípvolodimir ontheequivalenceofpolynomialmatricesoverafield
AT prokipv proekvívalentnístʹmnogočlennihmatricʹnadpolem
AT prokípvolodimir proekvívalentnístʹmnogočlennihmatricʹnadpolem

Ähnliche Einträge