|Revista Colombiana de Matemáticas|
Abstract. We define the outer energy of a real symmetric matrix M as for the eigenvalues l1, ¼, ln of M and their arithmetic mean . We discuss the properties of the outer energy in contrast to the inner energy defined as . We prove that Einn is the maximum among the energy functions e: S (n) ® R and Eout among functions , where f is an energy function. We prove a variant of the Coulson integral formula for the outer energy.