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Work supported in part by the Ministry of Science and Environmental Protection. Grant 1771.
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Section 22
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More About Geršgorin-type theorems
Article first published online: 27 DEC 2004
DOI: 10.1002/pamm.200410312
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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How to Cite
Cvetković, L. and Kostić, V. (2004), More About Geršgorin-type theorems. Proc. Appl. Math. Mech., 4: 662–663. doi: 10.1002/pamm.200410312
Publication History
- Issue published online: 27 DEC 2004
- Article first published online: 27 DEC 2004
- Abstract
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Abstract
In the recent book of R.S. Varga, [3], one of two main recurring themes is that a nonsingular theorem for matrices gives rise to an equivalent eigenvalue inclusion set in the complex plane, and conversely. If such nonsingularity result can be extended via irreducibility, usually this can be used for obtaining more information about the boundary of the corresponding eigenvalue inclusion set. Here we will start with one of Geršgorin-type theorem for eigenvalue inclusion, given in [1], (for which exists corresponding equivalent statement about nonsingularity of a particular class of matrices) and use it for proving necessary conditions for an eigenvalue to lie on the boundary of localization area. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)