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The estimates of diagonally dominant degree and eigenvalues distributions for the Schur complements of matrices
Abstract
The theory of Schur complement plays an important role in many fields such as matrix theory and control theory. In this paper, applying the properties of Schur complement and some inequality techniques, some new estimates of diagonally dominant degree on the Schur complement of matrices are obtained, which can improve considerably some previous results. As an application, we present some new distribution theorems for eigenvalues of the Schur complement. Finally, we give a numerical example to illustrate the advantages of our derived results.
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