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Monotone matrix functions of successive orders


Author: Suhas Nayak
Journal: Proc. Amer. Math. Soc. 132 (2004), 33-35
MSC (2000): Primary 15A48; Secondary 15A24, 47A63
DOI: https://doi.org/10.1090/S0002-9939-03-07218-6
Published electronically: July 17, 2003
MathSciNet review: 2021245
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Abstract: 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: snayak@stanford.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07218-6
Keywords: Monotone matrix functions, L\"{o}wner's Theorem, Sylvester's Determinant Identity
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
Article copyright: © Copyright 2003 American Mathematical Society