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 § 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

• 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

• P-matrix
• Z-matrix