New Perturbation Analysis of Generalized Singular Values of Grassmann Matrix Pairs with Arbitrary Permutation

Abstract

In this paper we give new perturbation analysis of generalized singular values of Grassmann matrix pairs with arbitrary permutation from a new perspective. The new explicit expressions of the chordal metric between generalized singular values of Grassmann matrix pairs with arbitrary permutation are presented, which result in only two small-size singular value decompositions to evaluate. The proposed results are generalizations of several results on bounds on perturbation of generalized singular values.