Finding relations between systems of entities: a multivariate approach

A procedure to find out the relationship between systems of entities is described. The crux of the approach depends on projecting the systems to be compared on the same arbitrary hyperspace so that any two systems of entities can be related. The procedure described applies to data presented in square or rectangular non-singular matrices and provides a procedure to determine multiple regression coefficients, multiple correlations, canonical correlations and the relationships between the inner product of the row vectors and of the column vectors of the matrices involved. The operations described apply to raw values, deviation or standard scores, and may help in interdisciplinary research, though the risks involved in the blind application of a mathematical abstract formulation should not be ignored.