In this paper, we introduce symmetric diagram matrices $A_{ s+r,s}$ of size ${ _{ (s+r)}}C_s$ whose entries are $\{ x_i\}_{ min\{ s,r\}}$. We compute the eigenvalues of symmetric diagram matrices using elementary row and column operations inductively. As a byproduct, we obtain the eigenvalues of Gram matrices of a larger class of diagram algebras like the signed partition algebras, algebra of $\mathbb{ Z}_2$ relations and partition algebras.
Categories: math.RA