  A new look on the principal component analysis has been presented. Firstly, a
geometric interpretation of determination coefficient was shown. In turn, the
ability to represent the analyzed data and their interdependencies in the form
of easy-to-understand basic geometric structures was shown. As a result of the
analysis of these structures it was proposed to enrich the classical PCA. In
particular, it was proposed a new criterion for the selection of important
principal components and a new algorithm for clustering primary variables by
their level of similarity to the principal components. Virtual and real data
spaces, as well as tensor operations on data, have also been identified.The
anisotropy of the data was identified too.
