On the extremal points of a class of polytopes of matrices (Q1183198)

Let \(M_ s(x)=\{A\in R^{n\times n}:A\geq 0\), \(A^ t=A\), \(Ae=x\}\), where \(x\) is a vector with positive entries. And let \(M(x)=\{A\in R^{n\times n}:A\geq 0\), \(Ae=x\), \(A^ te=x\}\). The authors prove that the extremal point of \(M_ s(x)\) can be written as the average of an extremal point of \(M(x)\) and its transpose. Some related results are obtained.