A network of chemical species and reactions can be described by the by stochiometry matrix . is the net number of species produced or consumed in reaction . The dynamics of the network are described by

where is the vector of species concentrations, is a vector of time independent parameters, and is time.

Each structural conservation, or interchangably, *conserved sum* (e.g. conserved moiety) in
the network coresponds to a lineraly dependent row in the stoichiometry matrix .

If there are conserved sums, then the row rank, of is , and
the stochiometry matrix may first be re-ordered such that the first are linearly
independent, and the remaining rows are linear combinations of the first
rows. The *reduced stochiometry matrix* is then formed from the first
rows of . Finally, may be expressed as a product of the
*link matrix* and the matrix:

The link matrix has the form

where is the identity matrix and is a matrix.

The following methods are related to the analysis of the stoichiometric matrix.