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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Geršgorin inclusion set for the field of values of a finite matrix


Author: Charles R. Johnson
Journal: Proc. Amer. Math. Soc. 41 (1973), 57-60
MSC: Primary 15A42
MathSciNet review: 0318191
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Abstract: An easily computed Geršgorin type inclusion set for the field of values of an $ n$ by $ n$ complex matrix is presented. Some functional properties of this inclusion set parallel those of the field of values, and illustrative examples are given.


References [Enhancements On Off] (What's this?)

  • [1] W. W. Parker, Sets of complex numbers associated with a matrix, Duke Math. J. 15 (1948), 711–715. MR 0026985 (10,230g)
  • [2] S. Geršgorin, Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR 7 (1931), 749-754.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0318191-3
PII: S 0002-9939(1973)0318191-3
Keywords: Geršgorin set, field of values, subadditive set valued function, spectrum, eigenvalues, numerical radius
Article copyright: © Copyright 1973 American Mathematical Society