Covariance matrices play the key role for dimension reduction in eigenspace projection methods for pattern recognition. Two scatters, an intraclass scatter and an interclass scatter, are obtained from samples for describing the sample distributions. The representation for these two scatters is classified into four categories. In this study, we focus on the analysis of the intraclass and interclass scatters. Three experiments, the evaluation for a music genre dataset, a bird sound dataset, and four face datasets, are conducted to make the comparisons of several state-of-the-art algorithms.