1880-1975. German mathematician.

Proved the Perron-Frobenius theorem (1907): every positive square matrix has a unique largest eigenvalue with a corresponding positive eigenvector.

This theorem guarantees that Markov chains on connected graphs converge to a unique stationary distribution — the mathematical foundation of PageRank and cyberank.

Without Perron-Frobenius, there is no guarantee that the focus distribution $\pi$ converges. With it, convergence is assured under ergodicity.

Contributed extensively to continuous fractions, differential equations, and non-negative matrices.

Professor at the University of Munich for over four decades.

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