Improving the Localization of Eigenvalues for Complex Matrices
Parviz Sargolzaei, R. Rakhshanipur · 2011
In this paper, we give a new bound for n � i=1 |λ i| 2 , which improves Schur, Kress, and Eberlein’s inequalities. By using this estimate, we provide disks and rectangles which include the eigenvalues of a complex matrix and then we compare these regions. Finally, we improve these regions by a strip for matrices with characteristic polynomial including real coefficients. Numerical examples are provided to illustrate the results in this contribution.