Perturbation Theorems for Generalized Singular Values

Abstract

Let $A$ and $B$ be $m×n$ and $p×n$ complex matrices respectively. This paper, as a continuation of the author's papers [7], discusses perturbation bounds for the generalized singular values of the Matrix-pair{$A$,$B$} in the case of rank$\left( \begin{array}{c} A \\ B \\ \end{array} \right)$＜$n$.