Abstract
New eigenvalue inclusion regions are given by establishing the necessary and sufficient conditions for two classes of nonsingular matrices, named double α1-matrices and double α2-matrices. These results are generalizations of Brauer’s eigenvalue localization theorem and improvements over the results in [L. Cvetkovic, V. Kostic, R. Bru, and F. Pedroche. A simple generalization of Gersgorin’s theorem. Adv. Comput. Math., 35:271–280, 2011.].
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