We provide necessary and sufficient conditions for the generalized (star operator)-Sylvester matrix equation, AXB+CX(star operator)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 operator)-Sylvester equations.
Solvability and uniqueness criteria for generalized Sylvester-type equations
Poloni, Federico;Robol, Leonardo
2018-01-01
Abstract
We provide necessary and sufficient conditions for the generalized (star operator)-Sylvester matrix equation, AXB+CX(star operator)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 operator)-Sylvester equations.File in questo prodotto:
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