Лінійні матричні різносторонні рівняння над квадратичними кільцями з інволюцією
Necessary and sufficient conditions for the existence of the Sylvester-type solutions of linear matrix equations over quadratic rings $K=\mathbb{Z}[\sqrt k]$ with involution are established. The criterion of the existence and uniqueness of integer solutions, that is, solutions over the ring of integ...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Ukrainian |
| Veröffentlicht: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2023
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| Schlagworte: | |
| Online Zugang: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2023.21.5-16 |
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| Назва журналу: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Zusammenfassung: | Necessary and sufficient conditions for the existence of the Sylvester-type solutions of linear matrix equations over quadratic rings $K=\mathbb{Z}[\sqrt k]$ with involution are established. The criterion of the existence and uniqueness of integer solutions, that is, solutions over the ring of integers $\mathbb{Z}$ of such equations, is indicated. The conditions are given in terms of the equivalence of matrices with elements from the ring of integers, which are constructed from the coefficients of the matrix equation using the Kronecker product of matrices. Cite as: H. V. Zelisko, N. B. Ladzoryshyn, V. M. Petrychkovych, “Linear matrix two-sided equations over quadratic rings with involution,” Prykl. Probl. Mekh. Mat., Issue 21, 5–16 (2023) (in Ukrainian), https://doi.org/10.15407/apmm2023.21.5-16 |
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