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Spectra of Nearly Hermitian Matrices

W. Kahan
Proceedings of the American Mathematical Society
Vol. 48, No. 1 (Mar., 1975), pp. 11-17
DOI: 10.2307/2040683
Stable URL: http://www.jstor.org/stable/2040683
Page Count: 7
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Spectra of Nearly Hermitian Matrices
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Abstract

When properly ordered, the respective eigenvalues of an n × n Hermitian matrix A and of a nearby non-Hermitian matrix A + B cannot differ by more than (log2 n + 2.038) |B|; moreover, for all n ≥ 4, examples A and B exist for which this bound is in excess by at most about a factor 3. This bound is contrasted with other previously published over-estimates that appear to be independent of n. Further, a bound is found, for the sum of the squares of respective differences between the eigenvalues, that resembles the Hoffman-Wielandt bound which would be valid if A + B were normal.

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