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 gx0 (x) is a monotone matrix function of order n for every value of x0 in I, assuming that f' is strictly positive on I.
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