On the maximal number of Pareto eigenvalues in a matrix of given order
Jean-Bernard Baillon, Alberto Seeger · Linear and Multilinear Algebra · 2019
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 cn be the maximal number of Pareto eigenvalues in a general matrix of order n. In this work, we show that c3=9 and improve the best known lower bounds for cn for intermediate values of n by 20–25%. We also study some recursive properties of the sequence {cn}n≥1.