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 | References | Similar Articles | Additional Information

Abstract: This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, , in where is an interval of the real line, is a monotone matrix function of order on if and only if a related, modified function is a monotone matrix function of order for every value of in , assuming that is strictly positive on .

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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