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Every n × n Matrix Z with Real Spectrum Satisfies |Z - Z*| ≤ |Z + Z*| (log2 n + 0.038)

W. Kahan
Proceedings of the American Mathematical Society
Vol. 39, No. 2 (Jul., 1973), pp. 235-241
DOI: 10.2307/2039622
Stable URL: http://www.jstor.org/stable/2039622
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Every n × n Matrix Z with Real Spectrum Satisfies |Z - Z*| ≤ |Z + Z*| (log2 n + 0.038)
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Abstract

The title's inequality is proved for the operator bound-norm in a unitary space. An example is exhibited to show that the inequality cannot be improved by more than about 8% when n is large. The numerical range, of an n × n matrix Z with real spectrum, is then shown to be not arbitrarily different in shape from the spectrum.

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