Q-matrix

In mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q.

Properties

M is a Q-matrix if there exists d > 0 such that LCP(M,0) and LCP(M,d) have a unique solution.^[1]^[2]
Any P-matrix is a Q-matrix. Conversely, if a matrix is a Z-matrix and a Q-matrix, then it is also a P-matrix.^[3]

↑ Karamardian, S. (1976). "An existence theorem for the complementarity problem". Journal of Optimization Theory and Applications. 19 (2): 227–232. doi:10.1007/BF00934094. ISSN 0022-3239. S2CID 120505258.
↑ Sivakumar, K. C.; Sushmitha, P.; Wendler, Megan (2020-05-17). "Karamardian Matrices: A Generalization of $Q$-Matrices". arXiv:2005.08171 [math.OC].
↑ Berman, Abraham. (1994). Nonnegative matrices in the mathematical sciences. Plemmons, Robert J. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 0-89871-321-8. OCLC 31206205.

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