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]
gollark: Not "literally the same".
gollark: C ftl (for the lose).
gollark: RUSTUST
gollark: It's evil *now* for ones who make complex applications.
gollark: Also not C, C is evil.

See also

References

  1. 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.
  2. Sivakumar, K. C.; Sushmitha, P.; Wendler, Megan (2020-05-17). "Karamardian Matrices: A Generalization of $Q$-Matrices". arXiv:2005.08171 [math].
  3. 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.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.