On the energy of symmetric matrices and Coulson's integral formula

We dene the outer energy of a real symmetric matrix M for the eigenvalues λ1, …, λn of M and their arithmetic mean λ(M). We discuss the properties of the outer energy in contrast to the inner energy defined as Einn(M) = ∑ni = 1 |λi|. We prove that Einn is the maximum among the energy functions e: S(...