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The spread of a matrix

Published online by Cambridge University Press:  26 February 2010

L. Mirsky
L. Mirsky
Affiliation:
The University, Sheffield.
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Extract

Although there is an extensive literature dealing with the location of characteristic roots of matrices, the problem of estimating the maximum distance between two characteristic roots of a given matrix does not appear to have attracted much attention. In the present note we shall be concerned with this problem.

Type
Research Article
Information
Mathematika , Volume 3 , Issue 2 , December 1956 , pp. 127 - 130
Copyright
Copyright © University College London 1956

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References

page 127 note † That is, A commutes with its transposed conjugate A*.

page 128 note † I am indebted to Mr. A. R. Curtis for suggesting a simplification in my original proof of the lemma.

page 129 note † See Schur, I., Math. Annalen, 66 (1909), 488–510.CrossRefGoogle Scholar

page 129 note ‡ Schur, op. cit.

page 130 note † Journal für Math., 137 (1910), 310–313.Google Scholar

page 130 note ‡ Duke Math. J., 15 (1948), 711–715CrossRefGoogle Scholar. The theorem in question states that every plane set of diameter I can be covered by a circle of radius. 3−3/2.