Q-matrix

This article is about the notion used in the context of linear complementarity problems. For the one used in the context of Markov-chain, see Continuous-time Markov chain.

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

References

Murty, Katta G. (January 1972). "On the number of solutions to the complementarity problem and spanning properties of complementary cones". Linear Algebra and its Applications. 5 (1): 65–108. doi:10.1016/0024-3795(72)90019-5.
Aganagic, Muhamed; Cottle, Richard W. (December 1979). "A note on Q-matrices". Mathematical Programming. 16 (1): 374–377. doi:10.1007/BF01582122.
Pang, Jong-Shi (December 1979). "On Q-matrices". Mathematical Programming. 17 (1): 243–247. doi:10.1007/BF01588247.
Danao, R. A. (November 1994). "Q-matrices and boundedness of solutions to linear complementarity problems". Journal of Optimization Theory and Applications. 83 (2): 321–332. doi:10.1007/bf02190060.

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