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Marshall, A.W., Olkin, I. and Arnold, B.C. (2011) Inequalities: Theory of Majorization and Its Applications. Springer Series in Statistics, 2nd Edition, Springer, New York.
https://doi.org/10.1007/978-0-387-68276-1

has been cited by the following article:

• TITLE: Bounding Inequalities for Eigenvalues of Principal Submatrices

  AUTHORS: Achiya Dax

  KEYWORDS: Cauchy Interlacing Theorem, Poincaré Interlacing Theorem, Ky Fan Trace Theorems, Non-Hermitian Matrices, Normal Matrices, Bounding Inequalities

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.9 No.2, June 30, 2019

  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.