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]

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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.

Murty, Katta G. (January 1972). "On the number of solutions to the complementarity problem and spanning properties of complementary cones" (PDF). Linear Algebra and Its Applications. 5 (1): 65–108. doi:10.1016/0024-3795(72)90019-5. hdl:2027.42/34188.
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