Commutativity and spectra of Hermitian matrices

  • So W
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Abstract

If two Hermitian matrices commute, then the eigenvalues of their sum are just the sums of the eigenvalues of the two matrices in a suitable order. Examples show that the converse is not true in general. In this paper, partial converses are obtained. The technique involves a characterization of the equality cases for Weyl's inequalities. Moreover, a new proof on the commutativity of two Hermitian matrices with property L and analogous results for the product of two positive definite Hermitian matrices are included. © 1994.

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Authors

  • Wasin So

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