In this paper, two new sufficient conditions for the unique solution of a Sylvester-like absolute value equation $AXB+C\left|X\right|D=E$ with $A,C\in {\mathbb{R}}^{m\times m}$, $B,D\in {\mathbb{R}}^{n\times n}$ and $E\in {\mathbb{R}}^{m\times n}$ 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.

中文翻译：

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平方西尔维斯特式绝对值方程唯一解的新充分条件

本文为类Sylvester绝对值方程的唯一解提供了两个新的充分条件 $\mathrm{一种}X乙+C\left|X\right|d=Ë$ 与 $\mathrm{一种}，C\in {\mathbb{[R}}^{米\times 米}$， $乙，d\in {\mathbb{[R}}^{ñ\times ñ}$ 和 $Ë\in {\mathbb{[R}}^{米\times ñ}$ 给出了 $\mathrm{一种}$ 和 $乙$是非单数的，与Hashemi（2021）发表的作品不同。当所涉及的矩阵为平方时，对于类Sylvester绝对值方程的唯一解，也获得了两个有用的充要条件，并且相应的计算复杂度是正切的。