Abstract
This paper suggests a generalization of the additive Weyl inequalities to the case of two square matrices of different orders. As a consequence of the generalized Weyl inequalities, a theorem describing the location of eigenvalues of a Hermitian matrix in terms of the eigenvalues of an arbitrary Hermitian matrix of smaller order is derived. It is demonstrated that the latter theorem provides a generalization of Kahan’s theorem on clustered eigenvalues. It is also shown that the theorem on extended interlacing intervals is another consequence of the generalized additive Weyl inequalities suggested. Bibliography: 7 titles.
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 49–59.
Translated by L. Yu. Kolotilina.
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Kolotilina, L.Y. A generalization of weyl’s inequalities with implications. J Math Sci 101, 3255–3260 (2000). https://doi.org/10.1007/BF02672770
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DOI: https://doi.org/10.1007/BF02672770