text: Suppose that a chemical system has  elements and  chemical species (elements or compounds). The latter are combinations of the former, and each species  can be represented as a sum of elements:
  where  are the integers denoting number of atoms of element  in molecule . Each species is determined by a vector (a row of this matrix), but the rows are not necessarily linearly independent. If the rank of the matrix is , then there are  linearly independent vectors, and the remaining  vectors can be obtained by adding up multiples of those vectors. The chemical species represented by those  vectors are components of the system.
  If, for example, the species are C (in the form of graphite), CO and CO, then
  Since CO can be expressed as CO = (1/2)C + (1/2)CO, it is not independent and C and CO can be chosen as the components of the system.
  There are two ways that the vectors can be dependent. One is that some pairs of elements always appear in the same ratio in each species. An example is a series of polymers that are composed of different numbers of identical units. The number of such constraints is given by . In addition, some combinations of elements may be forbidden by chemical kinetics. If the number of such constraints is , then
  Equivalently, if  is the number of independent reactions that can take place, then
  The constants are related by .