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.
Solvability and uniqueness criteria for generalized Sylvester-type equations
De Terán, Fernando
;Iannazzo, Bruno;Robol, Leonardo
2018
Abstract
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
