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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 382, Pages 104–124 (Mi znsl3864)  
On determinantal diagonal dominance conditions

L. Yu. Kolotilina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: The paper suggests sufficient nonsingularity conditions for matrices in terms of certain determinantal relations of diagonal dominance type, which improve and generalize some known results. These conditions are used to describe new eigenvalue inclusion sets and to derive new two-sided bounds on the determinants of matrices satisfying them. Bibl. 8 titles.
Key words and phrases: nonsingularity, Cramer's rule, diagonal dominance, minors, structured matrices, Gerschgorin's theorem, the Ostrowski–Brauer theorem, eigenvalue inclusion sets, bounds for determinants.
Received: 30.11.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 176, Issue 1, Pages 57–67
DOI: https://doi.org/10.1007/s10958-011-0393-8
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “On determinantal diagonal dominance conditions”, Computational methods and algorithms. Part XXIII, Zap. Nauchn. Sem. POMI, 382, POMI, St. Petersburg, 2010, 104–124; J. Math. Sci. (N. Y.), 176:1 (2011), 57–67
Citation in format AMSBIB
\Bibitem{Kol10}
\by L.~Yu.~Kolotilina
\paper On determinantal diagonal dominance conditions
\inbook Computational methods and algorithms. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 382
\pages 104--124
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3864}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 1
\pages 57--67
\crossref{https://doi.org/10.1007/s10958-011-0393-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958265638}
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