The C-matrix: Augmentation and reduction in the analysis of chemical composition and structure

• Composition of species and reactions are kept track of in matrices.
• The unified C-matrix method provides the detailed analysis of these matrices.
• It is based on augmenting each matrix by a unit matrix and reducing to RREF.
• We interpret the molecular, stoichiometric and Horiuti C-matrices in detail.

We propose a unified linear-algebraic approach that allows determining the three key matrices of chemical kinetics: molecular, stoichiometric and Horiuti matrix, all within a single procedure. This procedure is based on calculating a so called C-matrix, which is obtained from each matrix by augmenting it with a unit matrix and then reducing to Reduced Row Echelon Form (RREF). The procedure is rigorous and efficient to find answers to typical questions of chemical engineering and chemical kinetics, i.e., finding the independent components and reactions, expressing in them the dependent ones, and determining independent routes of complex chemical reactions as well. Contrary to the previous analysis procedures, the C-matrix contains all bookkeeping information on dependencies of components and elements, and their balances. The procedure can be used for developing new software tools in the analysis of complex chemical composition and networks.