佩龙一弗罗宾尼斯定理

In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron and extended by Georg Frobenius, asserts that a real square matrix with positive entries has a unique eigenvalue of largest magnitude and that eigenvalue is real. The corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory ; to the theory of dynamical systems ; to economics ;

to demography ;

to social networks ; to Internet search engines (PageRank); and even to the ranking of American football

teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau.