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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Stability of solutions of linear systems with dominant main diagonal


Author: Charles Kahane
Journal: Proc. Amer. Math. Soc. 33 (1972), 69-71
MSC: Primary 34D99
DOI: https://doi.org/10.1090/S0002-9939-1972-0294799-8
MathSciNet review: 0294799
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Abstract: We establish the asymptotic stability of solutions of a first order linear system of differential equations in which the matrix characterizing the system has a dominating principal diagonal with negative entries; the domination is expressed through the condition that, numerically, each entry in the principal diagonal exceeds the sum of the absolute values of the remaining entries in the same column.


References [Enhancements On Off] (What's this?)

  • [1] E. V. Haynsworth, Bounds for determinants with dominant main diagonal, Duke Math. J. 20 (1953), 199-209. MR 14, 837. MR 0053903 (14:837c)
  • [2] A. M. Ostrowski, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 3 (1952), 26-30. MR 14, 611. MR 0052380 (14:611c)
  • [3] G. Baley Price, Bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 2 (1951), 497-502. MR 12, 793. MR 0041093 (12:793c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294799-8
Keywords: Stability, linear differential system, matrices with dominant main diagonal
Article copyright: © Copyright 1972 American Mathematical Society

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