Abstract
A real square matrix A is called a Q-matrix if the linear complementarity problem LCP(A, q) has a solution for all . This means that for every vector q, there exists a vector x ≥ 0 such that y = Ax + q ≥ 0 and x T y = 0. Two new classes of matrices are studied, namely the Q #-matrices and -matrices. If for every vector q ∈ R(A), there exists a vector x ∈ R(A) satisfying x ≥ 0, y = Ax + q ≥ 0 and x T y = 0, then A is a Q #-matrix. If the vector x satisfying the above properties is instead required to be in R(A T ), then A is a -matrix. Properties of these classes of matrices and their relationship with the class of Q-matrices are studied.
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