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A simple proof of the Perron-Frobenius theorem for positive symmetric matrices

F Ninio

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An elementary proof is given that the statistical mechanical transfer matrix, when symmetric, has a maximum eigenvalue which is non-degenerate and larger than the absolute value of any other eigenvalue. Moreover, the corresponding eigenvector can be chosen so that all its entire entries are strictly positive.


PACS

02.10.Yn Matrix theory

02.10.Ud Linear algebra

MSC

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Dates

Issue 8 (August 1976)


A Corrigendum for this article has been published in 1977 J. Phys. A: Math. Gen. 10 1259


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