Let
G be a primitive strongly regular graph of order
n and
A is adjacency matrix.
In this paper we first associate to
A a real 3-dimensional Euclidean Jordan
algebra
with rank three spanned by
In and the natural powers of
A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of
order
n. Next we consider a basis
that is a Jordan frame of
. Finally,
by an algebraic asymptotic analysis of the second spectral decomposition of
some Hadamard series associated to
A we establish some inequalities over the
spectra and over the parameters of a strongly regular graph.