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

Abstract

We prove the minimax equality for the spectral radius of the product of matrices and , where and are compact sets of non-negative matrices of dimensions and , respectively, satisfying the so-called hourglass alternative.

Keywords:

• Matrix products
• non-negative matrices
• spectral radius
• minimax
• saddle point

AMS Subject Classifications:

• 15A45
• 15B48
• 49J35

Acknowledgements

The author is genuinely grateful to Eugene Asarin for numerous inspiring discussions and constructive criticism.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The work was carried out at the Institute of Radio-engineering and Electronics, Russian Academy of Sciences, and was supported by the Russian Science Foundation, Project number [16-11-00063].