A Note on Unique Solvability of the Absolute Value Equation

It is proved that applying sucient regularity conditions to the interval matrix[a ?? jbj;a + jbj], we can create a new unique solvability condition for the absolute valueequation ax + bjxj = b, since regularity of interval matrices implies unique solvability oftheir corresponding absolute value equation. this condition is formulated in terms of positivedeniteness of a certain point matrix. special case b = ??i is veried too as an application.