THE GEOMETRY OF THE HAUSDORFF DOMAIN IN LOCALIZATION PROBLEMS FOR THE SPECTRUM OF ARBITRARY MATRICES
A. A. Abdurakhmanov · Mathematics of the USSR-Sbornik · 1988
In this article it is shown that the Hausdorff domain (numerical range) is the union of the numerical ranges of a concretely constructed family of matrices acting in . 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.