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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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}},
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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/