An Euclidean Jordan Algebra of Symmetric Matrices Closed for the Schur Product

In this paper, we consider a particular real Euclidean Jordan algebras V of square real symmetric matrices closed for the Schur product of matrices such that its rank equals its dimension. Next, we present the definition of Krein parameters of the Euclidean Jordan algebra V and present some inequalities over these Krein parameters like those shown on Theorems 4.1, 4.2 and 4.3.