Pattern correlation matrices and their properties Original Research Article

This paper derives the Jordan block representation of the so-called pattern correlation matrices which appear in statistical analysis of random discrete sequences. A very explicit form of the row (or column) space of these matrices and of the similarity transformation to the transposed matrix is obtained. The covariance matrix of the joint distribution of frequencies of all patterns is expressed in terms of the pattern correlation matrix, and a simple generalized inverse of this covariance matrix is produced. The relevant statistical implications for goodness-of-fit testing are formulated.