Skip to main content
SpringerLink
Log in

On an inverse problem for nonnegative and eventually nonnegative matrices

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Let σ= (λ1,···λn)⊂C. We discuss conditions for which σ is the spectrum of a nonnegative or eventually nonnegative matrix. This brings us to study rational functions with nonnegative Maclaurin coefficients. A conjecture for special sets σ is stated and some evidence in support of this conjecture is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. G. Ciarlet,Some results in the theory of nonnegative matrices, Linear Algebra and Appl.1 (1968), 139–152.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Fiedler,Eigenvalues of nonnegative symmetric matrices, Linear Algebra and Appl.9 (1974), 119–142.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Frobenius,Über Matrizen aus nicht negativen Elementen, Sitzungsber. Preuss. Akad. Wiss. Berlin Math. Naturwiss, K1. (1912), 456–477.

  4. G. H. Hardy, J. E. Littlewood and G. Po'lya,Inequalities, second edition, Cambridge University Press, 1952.

  5. R. B. Kellog, Martices similar to a positive or essentially positive matrix, Linear Algebra and Appl.4 (1971), 191–204.

    Article  MathSciNet  Google Scholar 

  6. M. Newman,Nonnegative sums of roots of unity, National Bureau of Standards, preprint.

  7. H. Perfect,On positive stochastic matrices with real characteristic roots, Proc. Camb. Phil. Soc.48 (1952), 271–276.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Perfect,Methods of constructing certain stochastic matrices, Duke Math. J.20 (1953), 395–404.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Perfect,Methods of constructing certain stochastic matrices II, Duke Math. J.22 (1955), 305–311.

    Article  MATH  MathSciNet  Google Scholar 

  10. O. Perron,Über Matrizen, Math. Ann.64 (1907), 248–263.

    Article  MathSciNet  MATH  Google Scholar 

  11. F. L. Salzmann,A note on eigenvalues of nonnegative matrices, Linear Algebra and Appl.5 (1972), 329–338.

    MATH  MathSciNet  Google Scholar 

  12. A. Selberg, private communication.

  13. K. R. Suleimanova,Stochastic matrices with real characteristic values, Dokl. Akad. Nauk SSSR66 (1949), 343–345.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Shmuel Friedland

Authors
  1. Shmuel Friedland
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to my teacher Professor Menachem Schiffer on the occasion of his sixty-fifth birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Friedland, S. On an inverse problem for nonnegative and eventually nonnegative matrices. Israel J. Math. 29, 43–60 (1978). https://doi.org/10.1007/BF02760401

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760401

Keywords

Search

Navigation