The degree of an exact order matrix

The classes of exact order k matrices for any positive integer k, were defined and studied by Mohan, Parthasarathy and Sridhar. Here, we prove results on the linear complementarity problem LCQ (q, M), for M belonging to the class of exact order k, k greater than or equal to 3, using the concepts of degree theory. Our main result in this paper consists in proving that a matrix M is an element of R(nxn) of exact order k, for any positive integer n greater than or equal to k + 3, belongs to the class Q if and only if the degree of M is either +1 or −1. Also, a complete characterization of exact order 2 matrices is presented, in terms of their inverse structure.