  We consider small factor analysis models with one or two factors. Fixing the
number of factors, we prove a finiteness result about the covariance matrix
parameter space when the size of the covariance matrix increases. According to
this result, there exists a distinguished matrix size starting at which one can
determine whether a given covariance matrix belongs to the parameter space by
determining whether all principal submatrices of the distinguished size belong
to the corresponding parameter space. We show that the distinguished matrix
size is equal to four in the one-factor model and six with two factors.
