Istituto di Scienza e Tecnologie dell'Informazione     
De Terán F., Iannazzo B., Poloni F., Robol L. Solvability and uniqueness criteria for generalized Sylvester-type equations. In: Linear Algebra and Its Applications, [Online First 15 July 2017]
We provide necessary and sufficient conditions for the generalized $star$-Sylvester matrix equation, $AXB+CX^{star}D=E$, to have exactly one solution for any right-hand side $E$. These conditions are given for arbitrary coefficient matrices $A$, $B$, $C$, $D$ (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the existence and uniqueness of solution for generalized Sylvester and $star$-Sylvester equations.
URL: http://www.sciencedirect.com/science/article/pii/S0024379517304202
DOI: 10.1016/j.laa.2017.07.010
Subject Sylvester equation
Matrix pencil
Matrix equation
G.1.3 NUMERICAL ANALYSIS. Numerical Linear Algebra
15A22 Matrix pencils
15A24 Matrix equations and identities
65F15 Eigenvalues, eigenvectors

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