Some New Localization Results for Eigenvalues of Complex Matrices
Abstract
The localization of spectrum of complex-valued matrices is a foundational tool in matrix analysis and applied mathematics which offers a concise and computable descriptions on the location of spectrum in the complex plane. Many effective localization bounds, for instance, Gorgerin-type regions, and pseudo-spectrum allows to study and analyze the stability, sensitivity to perturbations, and spectral separation without full eigenvalue computation. In this paper, we present some new results on the localization of the spectrum of complex-valued matrices. Our approach is based on collection of various tools from matrix theory and numerical linear algebra. We have used MATLAB to demonstrate the localization of spectrum contained in the Gershgorin disks in the complex plane.