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Articles

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

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Pages 2356-2365 | Received 03 Oct 2016, Accepted 11 Dec 2016, Published online: 30 Dec 2016
 

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.

AMS Subject Classifications:

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].

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