This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study.

中文翻译：

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绝对值方程的独特可解性的表征：概述、扩展和未来方向

本文概述了保证绝对值方程唯一可解性的充要条件。除了讨论这些方程的基本形式之外，我们还讨论了几种概括，包括广义绝对值方程和矩阵绝对值方程。我们的调查涵盖了已知结果以及本研究中提出的新颖特征。