Spectral order preserving matrices and Muirhead’s theorem
Kong Ming Chong · Transactions of the American Mathematical Society · 1974
In this paper, a characterization is given for matrices which preserve the Hardy-Littlewood-Pólya spectral order relation $\prec$ for $n$-vectors in ${R^n}$. With this characterization, a new proof is given for the classical Muirhead theorem and some Muirhead-type inequalities are obtained. Moreover, sufficient conditions are also given for matrices which preserve the Hardy-Littlewood-Pólya weak spectral order relation $\prec \prec$.