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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1285–1302 (Mi izv1464)  

This article is cited in 8 scientific papers (total in 8 papers)

A generalization of Gershgorin's theorem

V. N. Solov'ev


Abstract: Estimates convenient for applicatins are obtained for the eigenvalues of complex matrices. Some applications in stability theory are indicated. The results are obtained by methods of convex analysis and the theory of nonnegative matrices.
Bibliography: 24 titles.

Full text: PDF file (1801 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 545–560

Bibliographic databases:

UDC: 518.512.25
MSC: Primary 15A18, 65F15; Secondary 15A42, 26B25, 34D20
Received: 15.07.1982

Citation: V. N. Solov'ev, “A generalization of Gershgorin's theorem”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1285–1302; Math. USSR-Izv., 23:3 (1984), 545–560

Citation in format AMSBIB
\Bibitem{Sol83}
\by V.~N.~Solov'ev
\paper A~generalization of Gershgorin's theorem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 6
\pages 1285--1302
\mathnet{http://mi.mathnet.ru/izv1464}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=727756}
\zmath{https://zbmath.org/?q=an:0572.65022|0551.65017}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 3
\pages 545--560
\crossref{https://doi.org/10.1070/IM1984v023n03ABEH001785}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Abdurakhmanov, “The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices”, Math. USSR-Sb., 59:1 (1988), 39–51  mathnet  crossref  mathscinet  zmath
    2. L. Naimark, E. Zeheb, “An extension of the Levy-Desplanque theorem and some stability conditions for matrices with uncertain entries”, IEEE Trans Circuits Syst I, 44:2 (1997), 167  crossref  mathscinet  zmath
    3. Bit-Shun Tam, Shangjun Yang, Xiaodong Zhang, “Invertibility of irreducible matrices”, Linear Algebra and its Applications, 259 (1997), 39  crossref
    4. Alan J. Hoffman, “Gersgorin variations I: on a theme of Pupkov and Solov'ev”, Linear Algebra and its Applications, 304:1-3 (2000), 173  crossref
    5. Yueting Yang, Chengxian Xu, “H-matrices and S-doubly diagonally dominant matrices”, Appl Math Chin Univ, 19:3 (2004), 349  crossref  mathscinet  zmath
    6. Michael R. Beran, Scott M. Cohen, “Phase boundaries in deterministic dense coding”, Phys Rev A, 79:3 (2009), 032307  crossref  isi
    7. Richard A. Brualdi, “Spectra of digraphs”, Linear Algebra and its Applications, 432:9 (2010), 2181  crossref
    8. Song-Ping Zhu, Wen-Ting Chen, “An inverse finite element method for pricing american options”, Journal of Economic Dynamics and Control, 2012  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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