Inference for isolated matrices and structured families of matrices

In this article we show how to use vec type operators to validate models for symmetric stochastic matrices. vec-type operators are operators that they also match vectors to matrices, that is, they allow to reorganize some elements of a matrix into a column vector. The presented formulation allowed us to make inference about the series of study, because the results presented in this work can be applied to the matrices of Hilbert-Schmidt products, that are very important matrices in the first phase of the STATIS methodology. Thus, the operators allowed us to present results that allow inference to be made for models for symmetric stochastic matrices. These models provided the basis for making inference for isolated matrices and structured families of matrices. In particular, we consider the case in which the matrices correspond to the treatments of base models. Thus, using the results presented, using vec type operators, it is possible to adjust a model with degree s. If λ_s = 0, the model can be simplified. These results, as already mentioned, can be applied to the matrices of Hilbert-Schmidt products (which are very important in the first phase of the STATIS Methodology), and to cross-product matrices which have an important role in inference.