Semi-central Bott–Duffin $(e,f)$-inverses
UDC 512.552 We study Bott–Duffin $(e,f)$-inverses in the context of left and right semi-central idempotents. A new class of generalized inverses named semi-central Bott–Duffin $(e,f)$-inverses is introduced and studied. An example is given to show that the Bott–Duffin $(e,f)$-inverses are not neces...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9380 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1861046672799301632 |
|---|---|
| author | Fang, Li Zhao, Liang Fang, Li Zhao, Liang |
| author_facet | Fang, Li Zhao, Liang Fang, Li Zhao, Liang |
| author_sort | Fang, Li |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-29T12:33:28Z |
| description | UDC 512.552
We study Bott–Duffin $(e,f)$-inverses in the context of left and right semi-central idempotents. A new class of generalized inverses named semi-central Bott–Duffin $(e,f)$-inverses is introduced and studied. An example is given to show that the Bott–Duffin $(e,f)$-inverses are not necessarily semi-central Bott–Duffin $(e,f)$-inverses. It is shown that the semi-central Bott–Duffin $(e,f)$-inverses exhibit additional properties beyond the properties of general Bott–Duffin $(e,f)$-inverses. As applications, we examine semi-central Bott–Duffin $(e,f)$-inverses for several classes of matrices. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9380 |
| first_indexed | 2026-03-29T01:00:26Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9380 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-30T01:00:13Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-93802026-03-29T12:33:28Z Semi-central Bott–Duffin $(e,f)$-inverses Semi-central Bott–Duffin $(e,f)$-inverses Fang, Li Zhao, Liang Fang, Li Zhao, Liang semi-central Bott-Duffin (e,f)-inverse, Bott-Duffin (e,f)-inverse, matrix algebra UDC 512.552 We study Bott–Duffin $(e,f)$-inverses in the context of left and right semi-central idempotents. A new class of generalized inverses named semi-central Bott–Duffin $(e,f)$-inverses is introduced and studied. An example is given to show that the Bott–Duffin $(e,f)$-inverses are not necessarily semi-central Bott–Duffin $(e,f)$-inverses. It is shown that the semi-central Bott–Duffin $(e,f)$-inverses exhibit additional properties beyond the properties of general Bott–Duffin $(e,f)$-inverses. As applications, we examine semi-central Bott–Duffin $(e,f)$-inverses for several classes of matrices. УДК 512.552 Напівцентральні $(e,f)$-обернені елементи Ботта–Даффіна Досліджено $(e,f)$-обернені елементи Ботта–Даффіна в контексті лівих і правих напівцентральних ідемпотентів. Введено та вивчено новий клас узагальнених обернених елементів, названих напівцентральними $(e,f)$-оберненими елементами Ботта–Даффіна. Наведено приклад, який показує, що $(e,f)$-обернені елементи Ботта–Даффіна не обов'язково є напівцентральними $(e,f)$-оберненими елементами Ботта–Даффіна. Показано, що напівцентральні $(e,f)$-обернені елементи Ботта–Даффіна мають додаткові властивості порівняно із загальними $(e,f)$-оберненими елементами Ботта–Даффіна. Як застосування розглянуто напівцентральні $(e,f)$-обернені елементи Ботта–Даффіна для кількох класів матриць. Institute of Mathematics, NAS of Ukraine 2026-03-28 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9380 10.3842/umzh.v78i3-4.9380 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 205–206 Український математичний журнал; Том 78 № 3-4 (2026); 205–206 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9380/10633 Copyright (c) 2026 Li Fang, Liang Zhao |
| spellingShingle | Fang, Li Zhao, Liang Fang, Li Zhao, Liang Semi-central Bott–Duffin $(e,f)$-inverses |
| title | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_alt | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_full | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_fullStr | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_full_unstemmed | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_short | Semi-central Bott–Duffin $(e,f)$-inverses |
| title_sort | semi-central bott–duffin $(e,f)$-inverses |
| topic_facet | semi-central Bott-Duffin (e,f)-inverse Bott-Duffin (e,f)-inverse matrix algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9380 |
| work_keys_str_mv | AT fangli semicentralbottduffinefinverses AT zhaoliang semicentralbottduffinefinverses AT fangli semicentralbottduffinefinverses AT zhaoliang semicentralbottduffinefinverses |