New sufficient conditions for the unique solution of a square Sylvester-like absolute value equation (Q2021453)

Assume that \(A, C\in\mathbb{R}^{m\times m}\), \(B, D\in\mathbb{R}^{n\times n}\) and \(F\in\mathbb{R}^{m\times n}\) are matrices and \(X\in\mathbb{R}^{m\times n}\) is an unknown matrix. The Sylvester-like absolute valued equation reads \[ AXB+C|X|D=F\,. \] Here, the authors give two sufficient conditions for the existence of a unique solution of the above equation. Some special cases are also considered.