Monotonicity of positive semidefinite Hermitian matrices
Russell Merris, Stephen J. Pierce · Proceedings of the American Mathematical Society · 1972
Inequalities which compare elements of the convex cone of positive semidefinite hermitian matrices with products of roots of elements are proved. They yield inequalities for Schur functions (generalized matrix functions) which, when specialized to the determinant, give a result of R. Bellman and L. Mirsky.