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. Surface micromachined mechanisms and micromotors

    M Mehregany and Yu-Chong Tai 1991 J. Micromech. Microeng. 1 73

  3. Heat-reflecting windows using gold and bismuth oxide films

    L Holland and G Siddall 1958 Br. J. Appl. Phys. 9 359

  4. News from the BIPM

    T J Quinn 2002 Metrologia 39 115

  5. Plasma uniformity in high-density inductively coupled plasma tools

    R A Stewart et al 1995 Plasma Sources Sci. Technol. 4 36

  6. Shanghai electron beam ion trap: design and current status

    Zhu Xikai et al 2004 J. Phys.: Conf. Ser. 2 65

  7. Numerical model for dynamic speckle: an approach using the movement of the scatterers

    Héctor J Rabal et al 2003 J. Opt. A: Pure Appl. Opt. 5 S381

  8. Nonlinear pulse compression by optical frequency mixing in crystals with second-order nonlinearity

    A Dubietis et al 1998 Pure Appl. Opt. 7 271

  9. An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel

    Stéphane Durand 2002 J. Opt. B: Quantum Semiclass. Opt. 4 S351

  10. How do biomolecular systems speed up and regulate rates?

    Huan-Xiang Zhou 2005 Phys. Biol. 2 R1

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.