Quick search Find article
Quick search
Find article

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

F Ninio

Show affiliations


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


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

    F Ninio 1976 J. Phys. A: Math. Gen. 9 1281

  2. Lévy flights: transitions and meta-stability

    Peter Imkeller and Ilya Pavlyukevich 2006 J. Phys. A: Math. Gen. 39 L237

  3. On superselection rules in Bohm–Bell theories

    Samuel Colin et al 2006 J. Phys. A: Math. Gen. 39 15403

  4. An algebraic geometric approach to integrable maps of the plane

    Danesh Jogia et al 2006 J. Phys. A: Math. Gen. 39 1133

  5. Quasi-periodic Green's functions of the Helmholtz and Laplace equations

    Alexander Moroz 2006 J. Phys. A: Math. Gen. 39 11247

  6. Applications of field-theoretic renormalization group methods to reaction–diffusion problems

    Uwe C Täuber et al 2005 J. Phys. A: Math. Gen. 38 R79

  7. Bell-type quantum field theories

    Detlef Dürr et al 2005 J. Phys. A: Math. Gen. 38 R1

  8. Generating function for Hermite–Gaussian modes propagating through first-order optical systems

    Martin J Bastiaans and Tatiana Alieva 2005 J. Phys. A: Math. Gen. 38 L73

  9. Maslov indices and monodromy

    H R Dullin et al 2005 J. Phys. A: Math. Gen. 38 L443

  10. O(N) symmetries, sum rules for generalized Hermite polynomials and squeezed states

    Jamil Daboul and Salomon S Mizrahi 2005 J. Phys. A: Math. Gen. 38 427

Users also read

What's this?
This innovative new feature generates a list of articles 'also read' by other users based on them reading the original article. Article abstracts citations and references are all considered and weighted accordingly. We hope that this will help you find relevant papers for your research.

  1. Comment on 'A simple proof of the Perron-Frobenius theorem for positive symmetric matrices'

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.