二重確率行列
出典: フリー百科事典『ウィキペディア(Wikipedia)』 (2016/05/09 14:58 UTC 版)
数学の確率論や組合せ論の分野における二重確率行列(にじゅうかくりつぎょうれつ、英: doubly stochastic matrix)とは、各行の和および各列の和がそれぞれ 1 となるような非負の実正方行列 のことを言う。すなわち、
- ^ Marshal, Olkin (1979). Inequalities: Theory of Majorization and Its Applications. pp. 8. ISBN 0-12-473750-1.
- ^ van der Waerden, B. L. (1926), “Aufgabe 45”, Jber. Deutsch. Math.-Verein. 35: 117.
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- ^ Egoryčev, G. P. (1980) (Russian), Reshenie problemy van-der-Vardena dlya permanentov, Krasnoyarsk: Akad. Nauk SSSR Sibirsk. Otdel. Inst. Fiz., p. 12, MR602332. Egorychev, G. P. (1981), “Proof of the van der Waerden conjecture for permanents” (Russian), Akademiya Nauk SSSR 22 (6): 65–71, 225, MR638007. Egorychev, G. P. (1981), “The solution of van der Waerden's problem for permanents”, Advances in Mathematics 42 (3): 299–305, doi:10.1016/0001-8708(81)90044-X, MR642395.
- ^ Falikman, D. I. (1981), “Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix” (Russian), Akademiya Nauk Soyuza SSR 29 (6): 931–938, 957, MR625097.
- ^ Fulkerson Prize, Mathematical Optimization Society, retrieved 2012-08-19.
- 1 二重確率行列とは
- 2 二重確率行列の概要
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