Quantum similarity and discrete representation of molecular sets

This study describes how quantum similarity theoretical framework can provide arbitrary molecular sets with discrete, general, unbiased, systematic and homogeneous numerical descriptions of their elements. Necessarily associated to quantum objects, such discrete descriptions can be related to a sequence of tensor collections of increasing rank. When choosing a specific tensor rank description of any molecular set, such a molecular descriptor set can be also considered a set of linearly independent arrays, which can act in turn as a basis set of some vector space of the appropriate dimension, equal to the cardinality of the supporting molecular set. Straightforward manipulation of the metric matrix of such tensor basis sets permits the ordering of the molecules in the set, among other interesting possibilities. Assorted Kruskal tree examples on Cramer steroid set are given.