Sufficient conditions for the unique solvability of absolute value matrix equations

In this paper, we discussed the unique solvability of the two absolute value matrix equations. The unique solvability condition $\rho (\mathrm{\mid }{A}^{-1}B\mathrm{\mid })<1$ is provided for the generalized absolute value matrix equation (GAVME) $AX+B\mathrm{\mid }X\mathrm{\mid }=F$. This condition is superior to that of Kumar et al. [J. Numer. Anal. Approx. Theory, 51(1) (2022) 83-87]. We also discussed different conditions for the unique solvability of the new generalized absolute value matrix equation (NGAVME) $AX+B\mathrm{\mid }CX\mathrm{\mid }=F$ with $A,B,C,F,X\in {\mathcal{R}}^{n\times n}$. We also provided the corrected version of Corollary 2.1 from the published work by Wang et al. [Appl. Math. Lett., 116 (2021) 106966].