On an Algorithm of G. Birkhoff Concerning Doubly Stochastic Matrices

On a Conjecture concerning Doubly Stochastic Matrices

On A Conjecture Concerning Doubly Stochastic Matrices

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...

On a Result of S. Sherman concerning Doubly Stochastic Matrices

He also defines, following Hardy, Littlewood and Polya [3] a partial ordering of w-dimensional real vectors: a<b if, and only if, there exists a d.s. matrix P such that a = Pb. In the above named article, the author investigates a conjecture of S. Kakutani to the effect that, if two d.s. matrices are such that Pi& <P3a for every real vector a, then Pi<P3. For this purpose he constructs a linear...

An Inequality for Doubly Stochastic Matrices *

Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron...

Doubly stochastic matrices of trees

In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices I...