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...

Let A ∈ Ωn be doubly-stochastic n × n matrix. Alexander Schrijver proved in 1998 the following remarkable inequality per(Ã) ≥ ∏ 1≤i,j≤n (1−A(i, j)); Ã(i, j) =: A(i, j)(1−A(i, j)), 1 ≤ i, j ≤ n (1) We prove in this paper the following generalization (or just clever reformulation) of (1): For all pairs of n × n matrices (P,Q), where P is nonnegative and Q is doublystochastic log(per(P )) ≥ ∑ 1≤i,...

Let A ∈ Ωn be doubly-stochastic n × n matrix. Alexander Schrijver proved in 1998 the following remarkable inequality per(Ã) ≥ ∏ 1≤i,j≤n (1−A(i, j)); Ã(i, j) =: A(i, j)(1−A(i, j)), 1 ≤ i, j ≤ n (1) We prove in this paper the following generalization (or just clever reformulation) of (1): For all pairs of n × n matrices (P,Q), where P is nonnegative and Q is doublystochastic log(per(P )) ≥ ∑ 1≤i,...

We prove that the set of n×n positive (row-)stochastic matrices and the corresponding set of doubly-stochastic matrices are asymptotically close. More specifically, random matrices within each of these classes are arbitrarily close in sufficiently high dimensions. AMS 2000 subject classifications:Primary 15A51,15A52,15A60, Stochastic Matrices. Let Sn denote the set of n × n stochastic matrices ...

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graphmatrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris’ question...