行随机矩阵中λ-极大矩阵的注记(英文)

A note of λ-maximizing matrices of row stochastic matrices

令Λn的所有元素之和为n的非负行随机方阵集合,λ是Λn上的实函数且λ(X)=∏nj=1∑ni=1xij-perX,X=[xij]∈Λn.一个矩阵A∈Λn称为Λn上的λ极大矩阵仅当对所有的X∈Λn,λ(A)≥λ(X).本文证明了A为Λn上的正λ极大矩阵时,必有λ(A)=1-n!nn及A=Jn.

Let Λ_n denote the set of all n-square nonnegative row stochastic matrices whose entries have sum n, and let λ be a real valued function on Λ_n defined by λ(X)=∏nj=1ni=1x_(ij)-perX for X=∈Λ_n. A matrix A∈Λ_n is called a λ-maximizing matrix on Λ_n if λ(A)≥λ(X) for all X∈Λ_n. In this paper, the following is proved that if A is a positive λ-maximizing matrix on Λ_n, then λ(A)=1-n!n^n and A=J_n.