Strong linear preservers of symmetric doubly stochastic or doubly substochastic matrices

AbstractLet S denote either the set of n×n symmetric doubly stochastic matrices or the set of n×n symmetric doubly substochastic matrices and let T be a linear map on span S. We prove that T(S)=S if and only if there exists an n×n permutation matrix P such that T(X)=PtXP for all X∈spanS. Our proofs make use of the concept of neighborly extreme points of a polytope and depend on some intricate graph theory