On the eigenvalues and diagonal entries of a Hermitian matrix

Abstract Suppose A is a hermitian matrix of order n . Let λ 1 ⩾ λ 2 ⩾ … ⩾ λ n and a 11 , …, a nn denote the eigenvalues and diagonal elements of A . If k n with Σ k i=1 λ i = Σ k i=1 a ii , what structure is imposed on the hermitian matrix? We prove that it must be block-diagonal.