Stability of solutions of linear systems with dominant main diagonal
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- by Charles Kahane
- Proc. Amer. Math. Soc. 33 (1972), 69-71
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294799-8
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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
- Emilie V. Haynsworth, Bounds for determinants with dominant main diagonal, Duke Math. J. 20 (1953), 199–209. MR 53903
- A. M. Ostrowski, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 3 (1952), 26–30. MR 52380, DOI 10.1090/S0002-9939-1952-0052380-7
- G. Baley Price, Bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 2 (1951), 497–502. MR 41093, DOI 10.1090/S0002-9939-1951-0041093-2
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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