Molecular spaces and the dimension paradox

In this study, the dimension or dimensionality paradox is defined and discussed in a dedicated context. This paradox appears when discrete vector representations of the elements of a molecular set are constructed employing several descriptor parameters, adopting specific values for each molecule. The dimension paradox consists in that when constructing discrete N-dimensional molecular vectors, the primal structure of the attached molecular set, chosen as a collection of different objects, cannot be well-defined if the number of descriptors N and the number of molecules M do not bear a convenient relation like: N >= M. This has implications for the linear independence of the vectors connected with each molecule.