A note on eigenvalues of perturbed 2x2 block Hermitian matrices

Abstract

Letbe two Hermitian matrices. We propose new perturbation bounds on the differences between the eigenvalues of and by the bounds of the eigenvector components. These results extend those of Nakatsukasa.

Keywords:

• Hermitian matrix
• eigenvalue
• perturbation bound
• 2x2 block

AMS Subject Classifications:

• 15A18
• 15A42
• 65F15

Acknowledgements

The authors would like to thank Prof. R.C. Li and the referee for their constructive suggestions and helpful comments, which led to significant improvement of the original manuscript.

Notes

The work was supported by the National Natural Science Foundation of China [grant number 11301056].