On sets of matrices having different spectrum maximizing products with unequal numbers of the same name factors

Autor:	Kozyakin, Victor
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Mathematics - Dynamical Systems Primary 15A18 Secondary 15A60 65F15
Druh dokumentu:	Working Paper
Popis:	Recently, J. Bochi and P. Laskawiec constructed an example of a set of matrices $\{A,B\}$ having two different (up to cyclic permutations of factors) spectrum maximizing products, $AABABB$ and $BBABAA$. In this paper, we identify a class of matrix sets for which the existence of at least one spectrum maximizing product with an odd number of factors automatically entails the existence of another spectrum maximizing product. Moreover, in addition to Bochi--Laskawiec's example, the number of factors of the same name (factors of the form $A$ or $B$) in these matrix products turns out to be different. The efficiency of the proposed approach is confirmed by constructing an example of a set of $2\times2$ matrices $\{A,B\}$ that has spectrum maximizing products of the form $BAA$ and $BBA$. Comment: Changed title, added 2 bibliography references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.10513 Zobrazit plný text záznamu View this record from Arxiv