The Unique Solvability Conditions for the Generalized Absolute Value Equations

This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) given by $Ax-B\mathrm{\mid }x\mathrm{\mid }=b$. Further, these conditions are also valid to determine the unique solution of the generalized absolute value matrix equations (GAVME) $AX-B\mathrm{\mid }X\mathrm{\mid }=F$. Finally, certain aspects related to the solvability and unsolvability of the absolute value equations (AVE) have been deliberated upon.