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.
  • 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.

See also

  • Murty, Katta G. (January 1972). (PDF). Linear Algebra and Its Applications. 5 (1): 65–108. doi:. hdl:.
  • Aganagic, Muhamed; Cottle, Richard W. (December 1979). "A note on Q-matrices". Mathematical Programming. 16 (1): 374–377. doi:. S2CID .
  • Pang, Jong-Shi (December 1979). "On Q-matrices". Mathematical Programming. 17 (1): 243–247. doi:. S2CID .
  • 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:. S2CID .