Models of Symmetric Stochastic Matrices

Abstract

Let M be a symmetric stochastic matrix with mean matrix ¹ then M = Xk j=1 ¸i®i®t i + ¹E With M = Pk j=1 ¸i®i®t i the spectral decomposition of the mean matrix of M: We consider the adjustment of the structure vector ¯i = ¸1=2 i ®i; i = 1; : : : ; k and model validation. Moreover we consider the especial case of cross prod- uct matrices XXt and XtX availing ourselves of the identity of non null eigenvalues of the matrices.