About some questions relative to the arbitrariness of signs: Their possible consequences in matrix signatures definition and quantum chemical applications

Abstract

The generalization of the arbitrary concept of sign to N-dimensional mathematical objects is discussed. Basically, the main argument employed here is founded in the previously described concepts of vector semispaces and their organization in shells. Usual operations in vector spaces are complemented by the inward matrix product, a matrix and vector product present within high level programming languages, as a sustentation of generalized signatures. It is shown how any vector space can be simply constructed from a simple set of convex positive definite mathematical objects. The sign generalization described here permits the definition of sign multiplets and signature support groups as a first step of deepening into the concept of general sign structures, which can be considered as possible conventions, situated far away from the classical Boolean sign structure. One can conclude that the study and use of sign generalization still is far to be complete. The theoretical set up developed in this way can be easily introduced in quantum chemistry wave function and density analysis.