The Q-property of a multiplicative transformation in semidefinite linear complementarity problems
R. Balaji, T. Parthasarathy · Electronic Journal of Linear Algebra · 2007
Abstract. The Q-property of a multiplicative transformation AXA T in semidefinite linear complementarity problems is characterized when A is normal. Key words. Multiplicative transformations, Q-property, Complementarity. AMS subject classifications. 90C33, 17C55. 1. Introduction. Let S n be the space of all real symmetric matrices of order n. Suppose that L: S n → S n is a linear transformation and Q ∈ S n.WewriteX ≽ 0, if X is symmetric and positive semidefinite. The semidefinite linear complementarity problem, SDLCP(L, Q) is to find a matrix X such that X ≽ 0, Y: = L(X)+Q ≽ 0, and XY =0.