| Authors: | Đorđević, Bogdan | Affiliations: | Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | The Equation AX−XB=C Without a Unique Solution: the Ambiguity Which Benefits Applications | Volume: | 20 | Issue: | 28 | First page: | 395 | Last page: | 442 | Related Publication(s): | Zbornik Radova | Issue Date: | 2022 | Rank: | M14 | ISBN: | 978-86-80593-75-3 | ISSN: | 0351-9406 | URL: | http://elib.mi.sanu.ac.rs/files/journals/zr/28/zrn28p395-442.pdf | Abstract: | This paper is a survey of the author's results regarding the equation AX-XB=C, in the case when it is without a unique solution. Sufficient conditions for the existence of infinitely many solutions are re-derived; methods for obtaining infinitely many solutions are revisited; some characterizations of the solution set are provided; the results are demonstrated on exact examples which require singularity of the initial equation. |
Keywords: | Sylvester equations | Lyapunov equations | matrix analysis | spectral theory | Fredholm theory | operator algebras | Publisher: | Mathematical Institute of the Sebian Academy of Sciences and Arts | Project: | The author is supported by the Ministry of Education, Sci- ence and Technological Development, Republic of Serbia, Grant No. 451-03-68/2022- 14/200029, and by the bilateral project between Serbia and Slovenia (Generalized inverses, operator equations and applications, Grant No. 337-00-21/2020-09/32) |
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