Yu. O. Vorontsov, Kh. D. Ikramov, “Conditions for unique solvability of the matrix equation <nobr>$AX+X^\ast B=C$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 5,Pages <nobr>775

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Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$

Yu. O. Vorontsov, Kh. D. Ikramov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

Key words: Sylvester matrix equations, equivalence transformations, regular pencil, Weierstrass canonical form, singular pencil, Kronecker canonical form.

UDC: 519.61