Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 50 [2] (2016)Páginas 173-186

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

J. A. de la Peña
Centro de Investigación en Matematicas, A.C., Guanajuato, Mexico
J. Rada
Universidad de Antioquia, Medelín, Colombia

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.

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