Characterizing Q-Matrices beyond L-Matrices

F. Flores-Bazán and R. López
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F. Flores-Bazán: Universidad de Concepción
R. López: Universidad de Concepción

Journal of Optimization Theory and Applications, 2005, vol. 127, issue 2, No 12, 447-457

Abstract: Abstract 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 $$q\in \mathbb{R}^{n}$$ , is discussed within such a new class. Positive subdefinite matrices with rank one are specially analyzed.

Keywords: Q-matrices; G-matrices; PSBD-matrices; complementarity problems (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-6554-5

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