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The minimum completions and covers of symmetric, Hankel symmetric, and centrosymmetric doubly substochastic matrices. (English) Zbl 1452.15024

Summary: In this paper, we investigate and describe all the minimal completions and covers of the symmetric, Hankel symmetric, and centrosymmetric doubly substochastic matrices, respectively.

MSC:

15B51 Stochastic matrices
15A15 Determinants, permanents, traces, other special matrix functions
15A69 Multilinear algebra, tensor calculus
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References:

[1] G. Birkhoff, Tres observaciones sobre el algebra lineal, Univ. Nac. Tucumán, Revista, Ser. A, 5 (1946), 147-151. · Zbl 0060.07906
[2] E. D. Bolker, Transportation polytopes, Journal of Combinatorial Theory, Series B, 13(3) (1972), 251-262. · Zbl 0241.90033 · doi:10.1016/0095-8956(72)90060-3
[3] R. A. Brualdi, Combinatorial Matrix Classes, Cambridge University Press, 2006. · Zbl 1106.05001
[4] R. A. Brualdi and L. Cao, Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices, (to appear). · Zbl 1400.15036 · doi:10.1007/s40306-018-0266-z
[5] L. Cao, S. Koyuncu, and T. Parmer, A mininal completion of doubly substochastic matrix, Linear and Multilinear Algebra, 64(11) (2016), 2313-2334. · Zbl 1358.15025 · doi:10.1080/03081087.2016.1155531
[6] A. L. Dulmage and N. S. Mendelsohn, The term and stochastic ranks of a matrix, Canadian Journal of Mathematics, 11(11) (1959), 269-279. · Zbl 0086.01802 · doi:10.4153/CJM-1959-029-8
[7] L. Mirsky, Proofs of two theorems on doubly-stochastic matrices, Proc. Amer. Math. Soc., 9.3 (1958), 371-374. · Zbl 0089.00902 · doi:10.1090/S0002-9939-1958-0095180-X
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