Could you suggest me a book where I can find a proof of Perron-Frobenius theorem (especially for nonnegative matrices) based on a Brouwer fixed point theorem?
2026-03-25 11:02:44.1774436564
Perron-Frobenius Theorem poof by Brouwer fixed point
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Since the OP is, according to one of her comments, looking for different proofs of the Perron-Frobenius theorem, it might be wortwhile to point out the following survey paper:
C. R. MacCluer: The many proofs and applications of Perron’s theorem, SIAM Rev. 42, No. 3, 487-498, 2000 (link to zbMATH).
While the paper deals mainly with matrices with positive entries, it contains a large list of references, and surely many of them also deal with non-negative matrices. For instance, a long list of references to proofs by means of Brouwer's fixed point theorem can be found on page 494.