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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

MIRANDA, HÉCTOR. DIAGONALS AND EIGENVALUES OF SUMS OF HERMITIAN MATRICES: EXTREME CASES. Proyecciones (Antofagasta) [online]. 2003, vol.22, n.2, pp.127-134. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172003000200003.

There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through con-gruences of the form UAU*+ V BV *; where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equal-ities are examined here

Keywords : Hermitian matrix; eigenvalues; diagonal elements.

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