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
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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