IEEE Transactions on Automatic Control, Vol.40, No.6, 1131-1133, 1995
A New Farkas Lemma for Positive Semidefinite Matrices
We consider a general linear system over the cone of positive semidefinite matrices. To check consistency, one may not invoke the standard Farkas Lemma because the cone of positive semidefinite matrices is not polyhedral, and thus an additional closedness assumption is required. In this note, we provide a modified Farkas Lemma with no closedness assumption.