In the present study, we introduce novel 3D protein descriptors based on the bilinear algebraic form in the ℝn space on the coulombic matrix. For the calculation of these descriptors, macromolecular vectors belonging to ℝn space, whose components represent certain amino acid side-chain properties, were used as weighting schemes. Generalization approaches for the calculation of inter-amino acidic residue spatial distances based on Minkowski metrics are proposed. The simple- and double-stochastic schemes were defined as approaches to normalize the coulombic matrix. The local-fragment indices for both amino acid-types and amino acid-groups are presented in order to permit characterizing fragments of interest in proteins. On the other hand, with the objective of taking into account specific interactions among amino acids in global or local indices, geometric and topological cut-offs are defined. To assess the utility of global and local indices a classification model for the prediction of the major four protein structural classes, was built with the Linear Discriminant Analysis (LDA) technique. The developed LDA-model correctly classifies the 92.6% and 92.7% of the proteins on the training and test sets, respectively. The obtained model showed high values of the generalized square correlation coefficient (GC2) on both the training and test series. The statistical parameters derived from the internal and external validation procedures demonstrate the robustness, stability and the high predictive power of the proposed model. The performance of the LDA-model demonstrates the capability of the proposed indices not only to codify relevant biochemical information related to the structural classes of proteins, but also to yield suitable interpretability. It is anticipated that the current method will benefit the prediction of other protein attributes or functions.