On the maximal number of Pareto eigenvalues in a matrix of given order. Issue 7 (19th May 2021) - Baillon, Jean-Bernard; Seeger, Alberto
ABSTRACT: How many Pareto eigenvalues can a matrix of prescribed order have? This question has been raised in a number of publications in the last two decades. Let c n be the maximal number of Pareto eigenvalues in a general matrix of order n . In this work, we show that c 3 = 9 and improve the best known lower bounds for c n for intermediate values of n by 20–25%. We also study some recursive properties of the sequence c n n ≥ 1 .