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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a hierarchy of generalized diagonal dominance properties for complex matrices
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by J. L. Brenner and W. G. Brown
Proc. Amer. Math. Soc. 25 (1970), 906-911
DOI: https://doi.org/10.1090/S0002-9939-1970-0260766-1

Abstract:

This article concerns dominance conditions for an $n \times m$ matrix. In the simplest kind of dominance, the (absolute) value of the diagonal element exceeds the sum of the absolute values of the nondiagonal elements on the same row. This condition has been generalized in the literature in several ways, of which we consider ways in which the rows of the matrix cooperate. Our work amounts to a sorting out of certain dominance conditions that belong to a class $\mathcal {C}$ of dominance conditions. We prove a theorem characterizing all true statements of the form \[ {C_1},{C_2}, \cdots ,{C_s} \Rightarrow {C_0}\] where ${C_i} \in \mathcal {C}(i = 0,1, \cdots ,s)$.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 906-911
  • MSC: Primary 15.58
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0260766-1
  • MathSciNet review: 0260766