Minimax theorem for the spectral radius of the product of non-negative matrices

Abstract

We prove the minimax equality for the spectral radius $\rho (AB)$ of the product of matrices $A\in \mathcal{A}$ and $B\in \mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are compact sets of non-negative matrices of dimensions $N\times M$ and $M\times N$, respectively, satisfying the so-called hourglass alternative.

11 pages, 15 bibliography references. Numerous style and grammar corrections, expanded the bibliography. arXiv admin note: text overlap with arXiv:1507.00492

References in corpus (3)

• Entropy Games and Matrix Multiplication Games
• Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matrices
• Constructive stability and stabilizability of positive linear discrete-time switching systems

Cited by in corpus (1)

• Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems