Let us interpret the vectors of the -dimensional Euclidean space in several ways as species (groups of atoms/functional bonds), reactions, mechanisms, measure units, etc.
Any linear (additive and homogeneous) quantity of any of these interpretations is, in fact a linear functional . Examples for such linear quantities are the molar volume, entalpy of formation, heat capacity, standard Gibbs free energy change (free entalpy) is the linear combination of the standard chemical potencials , heat of reactions, etc.
We call these functional in our presentation a valuation operator. Using the theory of linear functionals (esp. the Representation Theorem of F.Riesz) in linear algebra, we can investigate the structure of these linear functionals and may draw further conclusions.
These investigations serve a theoretical background for calculation methods already in use concerning valuation operators (increments/ linear functionals/ quantitative characteristics) in several fields of chemistry and physics.
|||Szalkai,I.: On valuation operators in stoichiometry and in reaction syntheses, J.Math. Chem. 27 (2000), 377-385|