Corrigendum to “Solvability and uniqueness criteria for generalized Sylvester-type equations”

We provide an amended version of Corollaries 7 and 9 in [De Terán, Iannazzo, Poloni, Robol, “Solvability and uniqueness criteria for generalized Sylvester-type equations”]. These results characterize the unique solvability of the matrix equation AXB+CX⋆D=E (where the coefficients need not be square) in terms of an equivalent condition on the spectrum of certain matrix pencils of the same size as one of its coefficients.