Counting Spectral Radii of Matrices with Positive Entries
da Silva, J. A. Dias · Freitas, Pedro J.
Original · EN
The sum-product conjecture of Erd os and Szemerédi states that, given a finite set A of positive numbers, one can find asymptotic lower bounds for {|A+A|,|A· A|} of the order of |A|¹⁺δ for every δ<1. In this paper we consider the set of all spectral radii of n× n matrices with entries in A, and find lower bounds for the cardinality of this set. In the case n=2, this cardinality is necessarily larger than {|A+A|,|A· A|}.
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