Characterizing Q-Matrices beyond L-Matrices

The characterization of Q-matrices, within the class of P₀ matrices due to Aganagič and Cottle, is well known. Afterward, Pang proved a similar characterization for the class L which does not contain class P₀. In this note, we establish furher the same result of Pang for a new class of matrices which properly contains class L. Furthermore, the equivalence between a Q-matrix and a Q_b-matrix, which consists of matrices such that the linear complementarity problem LCP(q,M) has a nonempty and compact solution set for all , is discussed within such a new class. Positive subdefinite matrices with rank one are specially analyzed. This work was supported by CONICYT-Chile through FONDECYT 104-0610, FONDAP-Matemáticas Aplicadas II, and Proyecto MECESUP UCO 9907.