Q-matrix

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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 § Definition.

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

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  • 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]

See also

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References

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  1. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  2. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  3. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).


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