A note on the unique solvability condition for generalized absolute value matrix equation

Abstract

The spectral radius condition \[\rho (\vert A^{-1} \vert\cdot \vert B \vert)<1\]for the unique solvability of generalized absolute value matrix equation (GAVME) \[AX + B \vert X \vert = D\] is provided. For some instances, our condition is superior to the earlier published singular values conditions \(\sigma_{\max}(\vert B \vert)<\sigma_{\min}(A)\) [M. Dehghan, 2020] and \(\sigma_{\max}(B)<\sigma_{\min}(A)\) [Kai Xie, 2021]. For the validity of our condition, we also provided an example.