New sufficient conditions for the unique solution of a square Sylvester-like absolute value equation

Abstract In this paper, two new sufficient conditions for the unique solution of a Sylvester-like absolute value equation A X B + C | X | D = E with A , C ∈ R m × m , B , D ∈ R n × n and E ∈ R m × n are given, where A and B are nonsingular, which are distinct from the published work by Hashemi (2021). When the involved matrices are square, two useful necessary and sufficient conditions for the unique solution of the Sylvester-like absolute value equation are obtained as well, and the corresponding computational complexity is sextic.