A unified treatment of some theorems on positive matrices

Letac, Gérard

doi:10.1090/S0002-9939-1974-0338037-8

A unified treatment of some theorems on positive matrices
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by Gérard Letac

Proc. Amer. Math. Soc. 43 (1974), 11-17

DOI: https://doi.org/10.1090/S0002-9939-1974-0338037-8

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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.

References

Henri Caussinus, Contribution à l’analyse statistique des tableaux de corrélation, Ann. Fac. Sci. Univ. Toulouse (4) 29 (1965), 77–182 (1966) (French). MR 242341
D. J. Hartfiel, Concerning diagonal similarity of irreducible matrices, Proc. Amer. Math. Soc. 30 (1971), 419–425. MR 281731, DOI 10.1090/S0002-9939-1971-0281731-5
David London, On matrices with a doubly stochastic pattern, J. Math. Anal. Appl. 34 (1971), 648–652. MR 281733, DOI 10.1016/0022-247X(71)90104-1

The permanent of a symmetric matrix

8

Alfréd Rényi, Foundations of probability, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1970. MR 0264723
R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
Richard Sinkhorn, A relationship between arbitrary positive matrices and doubly stochastic matrices, Ann. Math. Statist. 35 (1964), 876–879. MR 161868, DOI 10.1214/aoms/1177703591
Richard Sinkhorn, A relationship between arbitrary positive matrices and stochastic matrices, Canadian J. Math. 18 (1966), 303–306. MR 190160, DOI 10.4153/CJM-1966-033-9

Sur certaines variantes des projections du tableau d’échanges interindustriels

40

Note sur le remplissage d’un tableau à double entrée