Diagonals and eigenvalues of sums of hermitian matrices. Extreme cases

• Miranda, Héctor ^[1]
  1. [1] Universidad de Bío – Bío.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 22, Nº. 2, 2003, págs. 127-134
• Idioma: inglés
• DOI: 10.4067/S0716-09172003000200003
• Enlaces
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• Resumen

  • 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 congruences 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 equalities are examined here.

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