Solvability and uniqueness criteria for generalized Sylvester-type   equations
  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. 
Fernando De Ter\'an, Bruno Iannazzo, Federico Poloni, Leonardo Robol
math.RA math.FA math.NA