Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 0332820
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we derive sufficient conditions for a diagonally dominant reducible matrix to be nonsingular.

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

  • [1] R. Bellman, Introduction to matrix analysis, McGraw-Hill, New York, 1960. MR 23 #A153. MR 0122820 (23:A153)
  • [2] Ky Fan, Inequalities for sum of two $ M$-matrices, Inequalities I, Academic Press, New York and London, 1967, pp. 105-117. Edited by Oved Shisha. MR 0224632 (37:231)
  • [3] A. Ostrowski, On some conditions for nonvanishing of determinants, Proc. Amer. Math. Soc. 12 (1961), 268-273. MR 25 #1168. MR 0137719 (25:1168)
  • [4] -, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 3 (1952), 26-30. MR 14, 611. MR 0052380 (14:611c)
  • [5] O. Taussky, A recurring theorem on determinants, Amer. Math. Monthly 56 (1949), 672-676. MR 11, 307. MR 0032557 (11:307b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A15

Retrieve articles in all journals with MSC: 15A15

Additional Information

Keywords: Matrix, determinant, diagonally dominant, reducible, irreducible, nonsingular, $ M$-matrix
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society