Abstract
Let (A, B) and (C, D) be two \(n\times n\) and \(m\times m\) regular matrix pairs, respectively. The main contribution of this paper is to derive lower and upper bounds of the separation between (A, B) and (C, D) in terms of their generalized Schur decompositions and Weierstrass canonical forms. The results are illustrated by numerical examples.
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Acknowledgments
This work was done when the author was visiting University of Kansas during March-September 2013. The author is grateful to Professor Hongguo Xu for reading and commenting on the manuscript. The referee’s constructive comments for considerably improving the presentation are greatly appreciated.
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This work is supported by the Natural Science Foundation of Guangdong Province (S2013010012530).
