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A unified treatment of some theorems on positive matrices


Author: Gérard Letac
Journal: Proc. Amer. Math. Soc. 43 (1974), 11-17
MSC: Primary 15A48
DOI: https://doi.org/10.1090/S0002-9939-1974-0338037-8
MathSciNet review: 0338037
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Abstract | References | Similar Articles | Additional Information

Abstract: Various theorems on positive matrices are shown to be corollaries of one general theorem, the proof of which bears on Legendre functions, as used in Rockafellar's Convex analysis.


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  • [1] H. Caussinus, Contribution à l'analyse statistique des tableaux de corrélation, Ann. Fac. Sci. Univ. Toulouse (4) 29 (1965), 77-182. MR 39 #3672. MR 0242341 (39:3672)
  • [2] D. J. Hartfiel, Concerning diagonal similarity of irreducible matrices, Proc. Amer. Math. Soc. 30 (1971), 419-425. MR 43 #7446. MR 0281731 (43:7446)
  • [3] D. London, On matrices with a doubly stochastic pattern, J. Math. Anal. Appl. 34 (1971), 648-652. MR 43 #7448. MR 0281733 (43:7448)
  • [4] M. Marcus and M. Newman, The permanent of a symmetric matrix, Notices Amer. Math. Soc. 8 (1961), p. 595.
  • [5] A. Renyi, Foundations of probability, Holden-Day, San Francisco, Calif., 1970. MR 41 #9314. MR 0264723 (41:9314)
  • [6] R. T. Rockafellar, Convex analysis, Princeton Math. Series, no. 28, Princeton Univ. Press, Princeton, N.J., 1970. MR 43 #445. MR 0274683 (43:445)
  • [7] R. Sinkhorn, A relationship between arbitrary positive matrices and doubly stochastic matrices, Ann. Math. Statist. 35 (1964), 876-879. MR 28 #5072. MR 0161868 (28:5072)
  • [8] -, A relationship between arbitrary positive matrices and stochastic matrices, Canad. J. Math. 18 (1966), 303-306. MR 32 #7574. MR 0190160 (32:7574)
  • [9] P. Thionet, Sur certaines variantes des projections du tableau d'échanges interindustriels, Bull. Inst. Internat. Statist. 40 (1963), 431-446.
  • [10] -, Note sur le remplissage d'un tableau à double entrée, J. Soc. Statist. Paris, n$ ^\circ$ 10, 11, 12, (1964), 228-247.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0338037-8
Keywords: Positive matrices, entropy, gradient
Article copyright: © Copyright 1974 American Mathematical Society

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