Geodesic
Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 775-783 
Yu. O. Vorontsov; Kh. D. Ikramov. Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 775-783. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions for the unique solvability of the matrix equation $AX+X^\ast B=C$ are formulated in terms of the eigenvalues and the Kronecker structure of the matrix pencil $A+\lambda B^\ast$ associated with this equation.

[1] Ikramov Kh. D., “Ob usloviyakh odnoznachnoi razreshimosti matrichnogo uravneniya $AX+X^TB=C$”, Dokl. RAN, 430:4 (2010), 444–447 | MR | Zbl

[2] Ikramov Kh. D., Vorontsov Yu. O., “Ob odnoznachnoi razreshimosti matrichnogo uravneniya $AX+X^TB=C$ v singulyarnom sluchae”, Dokl. RAN, 438:5 (2011), 599–602 | MR | Zbl

[3] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966 | MR

[4] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl

[5] Ikramov Kh. D., “Matrichnye puchki — teoriya, prilozheniya, chislennye metody”, Itogi nauki i tekhniki. Ser. Matem. analiz, 29, VINITI, M., 1991, 3–106