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.
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].