A sufficient condition for nonvanishing of determinants
Authors:
P. N. Shivakumar and Kim Ho Chew
Journal:
Proc. Amer. Math. Soc. 43 (1974), 63-66
MSC:
Primary 15A15
DOI:
https://doi.org/10.1090/S0002-9939-1974-0332820-0
MathSciNet review:
0332820
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Abstract | References | Similar Articles | Additional Information
Abstract: In this note we derive sufficient conditions for a diagonally dominant reducible matrix to be nonsingular.
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- [3] A. M. Ostrowski, On some conditions for nonvanishing of determinants, Proc. Amer. Math. Soc. 12 (1961), 268–273. MR 137719, https://doi.org/10.1090/S0002-9939-1961-0137719-1
- [4] A. M. Ostrowski, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 3 (1952), 26–30. MR 52380, https://doi.org/10.1090/S0002-9939-1952-0052380-7
- [5] Olga Taussky, A recurring theorem on determinants, Amer. Math. Monthly 56 (1949), 672–676. MR 32557, https://doi.org/10.2307/2305561
-matrices, Inequalities I, Academic Press, New York and London, 1967, pp. 105-117. Edited by Oved Shisha. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A15
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0332820-0
Keywords:
Matrix,
determinant,
diagonally dominant,
reducible,
irreducible,
nonsingular,
-matrix
Article copyright:
© Copyright 1974
American Mathematical Society
