DIAGONALS AND EIGENVALUES OF SUMS OF HERMITIAN MATRICES: EXTREME CASES
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...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2003
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200003 |
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| Sumario: | 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 |
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