Euclidean Jordan algebras, MacLaurin series and inequalities on strongly regular graphs
Abstract
Let X be a strongly regular graph, whose adjacency matrix A has three distinct eigenvalues, and let V be the Euclidean Jordan algebra of real symmetric matrices, with the vector product and the inner product being the Jordan product and the usual trace of matrices, respectively. We consider the Euclidean Jordan subalgebra A of V spanned by the identity matrix and the natural powers of A. In this paper we work with the MacLaurin series of the sin function of some idempotents of A to obtain some inequalities over the parameters of X.
 Publication:

11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013
 Pub Date:
 October 2013
 DOI:
 10.1063/1.4825821
 Bibcode:
 2013AIPC.1558.1554D