Collective Euclidian distances and quantum similarity

A simple algorithm to find out a collective distance between arbitrary assemblies of points in some vector space is defined at various levels of complexity. The most straightforward procedure is related to a sum of Euclidian distances, which can be easily obtained from any Gram matrix of the point vectors. Similar but more involved formulation can be obtained with the tensor products of an indefinite number of vectors. Simple and elaborate examples are provided to illustrate the procedures along the text. The use of collective distances in reference to quantum similarity is discussed as an important application issue and a numerical example given.