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The diagonal equivalence of a nonnegative matrix to a stochastic matrix. (English) Zbl 0231.15017

MSC:
15B51 Stochastic matrices
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[1] Sinkhorn, R, A relationship between arbitrary positive matrices and doubly stochastic matrices, Ann. math. stat., 35, 876-879, (1964) · Zbl 0134.25302
[2] \scM. Marcus and M. Newman, unpublished paper.
[3] \scJ. Maxfield and H. Minc, unpublished paper.
[4] \scM. V. Menon. Reduction of a matrix with positive elements to a doubly stochastic matrix. Proc. Amer. Math. Soc., to appear. · Zbl 0153.05301
[5] Perfect, H; Mirsky, L, The distribution of positive elements in doubly stochastic matrices, J. London math. soc., 40, 688-698, (1965) · Zbl 0166.03501
[6] Morishima, M, Generalizations of the Frobenius-Wielandt theorems for nonnegative square matrices, J. London math. soc., 36, 211-220, (1961) · Zbl 0104.01301
[7] Thompson, A.C, On the eigenvectors of some not-necessarily-linear transformations, (), 577-598 · Zbl 0141.32501
[8] \scR. Sinkhorn and P. Knopp. Concerning nonnegative matrices and doubly stochastic matrices. To appear. · Zbl 0152.01403
[9] Marcus, M; Minc, H, A survey of matrix theory and matrix inequalities, (1964), Allyn and Bacon Boston · Zbl 0126.02404
[10] \scS. Karlin and L. Nirenberg. Remark on the paper of P. Nowosad. J. Math. Anal. Appl., to appear. · Zbl 0165.45802
[11] Gantmacher, F.R, ()
[12] Wielandt, H, Unzerlegbare, nicht negative matrizen, Math. Z., 52, 642-648, (1950) · Zbl 0035.29101
[13] Sinkhorn, R, A relationship between arbitrary positive matrices and stochastic matrices, Can. J. math., 18, 303-306, (1966) · Zbl 0136.24803
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