Strong linear preservers of symmetric doubly stochastic or doubly substochastic matrices

摘要

Let Y denote either the set of n x n symmetric doubly stochastic matrices or the set of n x it symmetric doubly substochastic matrices and let T be a linear map on span Y. We prove that T(Y) = Y if and only if there exists an n x n permutation matrix P such that T(X) = (PXP)-X-t forall X E span Y. Our proofs make use of the concept of neighborly extreme points of a polytope and depend on some intricate graph theory. (C) 2003 Elsevier tnc. All rights reserved. [References: 7]