Geodesic
The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices
Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 39-51 
A. A. Abdurakhmanov. The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices. Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 39-51. http://geodesic.mathdoc.fr/item/SM_1988_59_1_a2/
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     title = {The geometry of the {Hausdorff} domain in localization problems for the spectrum of arbitrary matrices},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article it is shown that the Hausdorff domain (numerical range) $W(A)=\{(Ax,x):\|x\|=1\}$ is the union of the numerical ranges of a concretely constructed family of matrices acting in $\mathbf C^2$. In other words, a certain method of descent of the numerical range is justified. This method is used to study localizations for the spectra of arbitrary matrices. As a result, generalizations are discovered for results of Johnson, Gershgorin–Solov'ev, Hirsch and Bendixson, and Mees and Atherton. Bibliography: 20 titles.

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