Dual systems for minor and principal component computation

Converting principal component dynamical system to a minor component dynamical system and vice versa sometimes leads to unstable systems. In this paper, classes of globally stable dynamical systems that can be converted between PCA and MCA systems by merely switching the signs of some terms of a given system are developed. These systems are shown to be applicable to symmetric and nonsymmetric matrices. These systems are then modified to be asymptotically stable by adding a penalty term. The proposed systems may apply to both the standard and the generalized eigenvalue problems. Lyapunov stability theory and LaSalle invariance principle are used to derive invariant sets for these systems.