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On the dimension of orbits of matrix pencils under strict equivalence
Journal
Applied Mathematics Letters
100
Author
De Terán Fernando
Dopico Froilán M.
Pagacz Patryk
Volume
172
Article ID
109695
ISSN
0893-9659
Access date
2025-08-26
Language
English
Journal language
English
Abstract in English
We prove that, given two matrix pencils 𝐿 and 𝑀, if 𝑀 belongs to the closure of the orbit of 𝐿 under strict equivalence, then the dimension of the orbit of 𝑀 is smaller than or equal to the dimension of the orbit of 𝐿, and the equality is only attained when 𝑀 belongs to the orbit of 𝐿. Our proof uses only the majorization involving the eigenstructures of 𝐿 and 𝑀 which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture.
Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
| dc.abstract.en | We prove that, given two matrix pencils 𝐿 and 𝑀, if 𝑀 belongs to the closure of the orbit of 𝐿 under strict equivalence, then the dimension of the orbit of 𝑀 is smaller than or equal to the dimension of the orbit of 𝐿, and the equality is only attained when 𝑀 belongs to the orbit of 𝐿. Our proof uses only the majorization involving the eigenstructures of 𝐿 and 𝑀 which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture. | |
| dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | |
| dc.contributor.author | De Terán, Fernando | |
| dc.contributor.author | Dopico, Froilán M. | |
| dc.contributor.author | Pagacz, Patryk - 106982 | |
| dc.date.accession | 2025-08-26 | |
| dc.date.accessioned | 2025-08-26T07:25:43Z | |
| dc.date.available | 2025-08-26T07:25:43Z | |
| dc.date.createdat | 2025-08-13T06:08:23Z | en |
| dc.date.issued | 2026 | |
| dc.date.openaccess | 0 | |
| dc.description.accesstime | w momencie opublikowania | |
| dc.description.sponsorshipidub | idub_yes | |
| dc.description.version | ostateczna wersja wydawcy | |
| dc.description.volume | 172 | |
| dc.identifier.articleid | 109695 | |
| dc.identifier.doi | 10.1016/j.aml.2025.109695 | |
| dc.identifier.issn | 0893-9659 | |
| dc.identifier.uri | https://ruj.uj.edu.pl/handle/item/559303 | |
| dc.language | eng | |
| dc.language.container | eng | |
| dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | |
| dc.rights.licence | CC-BY | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | |
| dc.share.type | inne | |
| dc.subtype | Article | |
| dc.title | On the dimension of orbits of matrix pencils under strict equivalence | |
| dc.title.journal | Applied Mathematics Letters | |
| dc.type | JournalArticle | |
| dspace.entity.type | Publication | en |
dc.abstract.en
We prove that, given two matrix pencils 𝐿 and 𝑀, if 𝑀 belongs to the closure of the orbit of 𝐿 under strict equivalence, then the dimension of the orbit of 𝑀 is smaller than or equal to the dimension of the orbit of 𝐿, and the equality is only attained when 𝑀 belongs to the orbit of 𝐿. Our proof uses only the majorization involving the eigenstructures of 𝐿 and 𝑀 which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture. dc.affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki dc.contributor.author
De Terán, Fernando dc.contributor.author
Dopico, Froilán M. dc.contributor.author
Pagacz, Patryk - 106982 dc.date.accession
2025-08-26 dc.date.accessioned
2025-08-26T07:25:43Z dc.date.available
2025-08-26T07:25:43Z dc.date.createdaten
2025-08-13T06:08:23Z dc.date.issued
2026 dc.date.openaccess
0 dc.description.accesstime
w momencie opublikowania dc.description.sponsorshipidub
idub_yes dc.description.version
ostateczna wersja wydawcy dc.description.volume
172 dc.identifier.articleid
109695 dc.identifier.doi
10.1016/j.aml.2025.109695 dc.identifier.issn
0893-9659 dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/559303 dc.language
eng dc.language.container
eng dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa dc.rights.licence
CC-BY dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl dc.share.type
inne dc.subtype
Article dc.title
On the dimension of orbits of matrix pencils under strict equivalence dc.title.journal
Applied Mathematics Letters dc.type
JournalArticle dspace.entity.typeen
Publication Affiliations
No affiliation
De Terán, Fernando
Dopico, Froilán M.
Wydział Matematyki i Informatyki
Pagacz, Patryk
mathematics
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