The Unique Solvability Conditions for the Generalized Absolute Value Equations

Abstract

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