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Bounding Inequalities for Eigenvalues of Principal Submatrices
Hydrological Service, Jerusalem, Israel
- 1 Hydrological Service, Jerusalem, Israel
Advances in Linear Algebra & Matrix Theory·Volume 09 (2019)·Pages 21–34·Published 30 June 2019·DOI10.4236/alamt.2019.92002
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Abstract
Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which extend these theorems. The new inequalities are obtained from the old ones by replacing eigenvalues and diagonal entries with their moduli. This modification yields effective bounding inequalities which are valid on a larger range of matrices.
KeywordsCauchy Interlacing TheoremPoincar&#233Interlacing TheoremKy Fan Trace TheoremsNon-Hermitian MatricesNormal MatricesBounding Inequalities
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