Geodesic
The Equation $\boldsymbol{AX-XB=C}$ Without a Unique Solution: the Ambiguity Which Benefits Applications
Zbornik radova, Tome 20 (2022) no. 28, p. 395 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 47-02, 47A62, 47A53, 47A60, 47L30, 46G05
Keywords: Sylvester equations, Lyapunov equations, matrix analysis, spectral theory, Fredholm theory, operator algebras 
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     author = {Bogdan D. Djordjevi\'c},
     title = {The {Equation} $\boldsymbol{AX-XB=C}$ {Without} a {Unique} {Solution:} the {Ambiguity} {Which} {Benefits} {Applications}},
     journal = {Zbornik radova},
     pages = {395 },
     year = {2022},
     volume = {20},
     number = {28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_2022_20_28_a9/}
}
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Bogdan D. Djordjević. The Equation $\boldsymbol{AX-XB=C}$ Without a Unique Solution: the Ambiguity Which Benefits Applications. Zbornik radova, Tome 20 (2022) no. 28, p. 395 . http://geodesic.mathdoc.fr/item/ZR_2022_20_28_a9/