On the maximal number of Pareto eigenvalues in a matrix of given order. Issue 7 (19th May 2021)

• Record Type: Journal Article
• Authors: Baillon, Jean-Bernard; Seeger, Alberto
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 7(2021)
• Page Start: 1185
• Page End: 1207
• Publication Date: 2021-05-19
• Subjects: Complementarity eigenproblem -- Pareto eigenvalue -- cardinality of Pareto spectra; 15A18 -- 15A39 -- 65H17; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1624681
• Languages: English
• ISSNs: 0308-1087

Abstract

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 .