aequationes mathematicae

, Volume 2, Issue 2–3, pp 319–326 | Cite as

A special class of doubly stochastic matrices

  • Alan J. Hoffman
Research Papers

Keywords

Special Class Stochastic Matrice 
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References

  1. [1]
    Bellman, R. andHoffman, A.,On a Theorem of Ostrowski and Taussky, Arch. Math. Basel5, 123–127 (1954).Google Scholar
  2. [2]
    Birkhoff, G.,Tres observaciones sobre el algebra lineal, Univ. Nac. Tucuman Rev. [Ser. A]5, 147–150 (1946).Google Scholar
  3. [3]
    Hardy, G. H., Littlewood, J. E., andPolya, G.,Some Simple Inequalities Satisfied by Convex Functions, Messenger of Math.58, 145–152 (1929);Inequalities (Cambridge 1934).Google Scholar
  4. [4]
    Hoffman, A. J.,On an Inequality of Hardy, Littlewood and Polya, Nat. Bur. Standards, Report No. 2977 (1953).Google Scholar
  5. [5]
    Mirsky, L.,Results and Problems in the Theory of Doubly-Stochastic Matrices, Z. Wahrscheinlichkeitstheorie und verw. Gebiete1, 319–334 (1963).Google Scholar
  6. [6]
    Ostrowski, A.,Sur quelques applications des fontions convexes et concaves au sens de I. Schur, J. Math. Pures Appl.31, 253–292 (1952).Google Scholar
  7. [7]
    Ostrowski, A. andTaussky, O.,On the Variation of the Determinant of a Positive Definite Matrix, Nederl. Wetensch. Proc. [Ser. A]54, 383 (1951).Google Scholar
  8. [8]
    Rado, R.,An Inequality, J. London Math. Soc.27, 1–6 (1952).Google Scholar
  9. [9]
    Guillemin, E. A.,On the Analysis and Synthesis of Single-Element-Kind Networks, IRE Trans., CT-7, 303–312 (1960).Google Scholar
  10. [10]
    Weinberg, L.,A Survey of Linear Graphs: Fundamentals and Applications to Network Theory, Matrix Tensor Quart. 81–89, 103–115 (1964).Google Scholar

Copyright information

© Birkhäuser Verlag 1968

Authors and Affiliations

  • Alan J. Hoffman
    • 1
  1. 1.Thomas J. Watson Research CenterNew YorkUSA

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