Bounding Inequalities for Eigenvalues of Principal Submatrices
Achiya Dax · Advances in Linear Algebra & Matrix Theory · 2019
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.