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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Monotone matrix functions of successive orders
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by Suhas Nayak PDF
Proc. Amer. Math. Soc. 132 (2004), 33-35 Request permission


This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, $f(x)$, in $C^3(I)$ where $I$ is an interval of the real line, is a monotone matrix function of order $n+1$ on $I$ if and only if a related, modified function $g_{x_0}(x)$ is a monotone matrix function of order $n$ for every value of $x_0$ in $I$, assuming that $f’$ is strictly positive on $I$.
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Additional Information
  • Suhas Nayak
  • Affiliation: Department of Mathematics, Caltech, Pasadena, California
  • Address at time of publication: Department of Mathematics, Stanford University, Stanford, California 94305-2125
  • Email:
  • Received by editor(s): August 25, 2002
  • Published electronically: July 17, 2003
  • Additional Notes: This work was conducted as part of a senior thesis at the California Institute of Technology
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 33-35
  • MSC (2000): Primary 15A48; Secondary 15A24, 47A63
  • DOI:
  • MathSciNet review: 2021245