On A Conjecture Concerning Doubly Stochastic Matrices
نویسندگان
چکیده
In a 2002 paper, Kirkland showed that if T ∈ Rn×n is an irreducible stochastic matrix with stationary distribution vector πT , then for A = I − T , maxj=1,...,n πj‖A j ‖∞ ≥ n−1 n , where Aj , j = 1, . . . , n, are the (n − 1) × (n − 1) principal submatrices of A obtained by deleting the j–th row and column of A. He also conjectured that equality holds in that lower bound if and only if either T is a permutation matrix ∗NSERC Grant No. OGP0138251. †Corresponding author. E-mail: [email protected], Phone: +1 (860) 4861290, Fax: +1 (860) 486-4238.
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