On symmetric functions of the eigenvalues of the sum of two Hermitian matrices

AbstractLet A and B be hermitian matrices with given eigenvalues (a1,…an) and (b1,…bn) respectively. Let (t1,…tn) be the eigenvalues of A + B. We establish that ∏j=1n(λ + tj) ϵ co ∏j=1n(λ + aj+bσ(j)); σ ϵ Sn where co denotes the convex hull in the space of polynomials and Sn denotes the permutation group on {1,…,n}