For a given complex matrix we describe new methods for localizing the eigenvalues and new upper bounds for the spread. These methods and upper bounds are sharper than those previously known.

http://iopscience.iop.org/article/10.1070/IM2015v079n01ABEH002739/pdf

Localization of eigenvalues and estimation of the spread for complex matrices

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Localization of eigenvalues and estimation of the spread for complex matrices