The conservation of mass within any mineral that is regarded as a closed system is expressed by the equations: ∑ j=i n a ijx j = b i, i = 1, 2,…m, or A x = b where a ij is the number of moles of oxide i in molecular member j, x i is the mole per cent of molecular member j in the mineral phase, and b i is the total number of moles of oxide i. Each of the column vectors a 1, a 2, … a n within the matrix of detached coefficients, A, represents a molecular member. If all possible molecular members of a given mineral group are grouped together in a matrix, B, the maximum number of members necessary to represent a mineral is equal to the rank of B, i.e. to the number of linearly independent column vectors in B. There are at most m − 1 such vectors. Once A is formed by arbitrarily selecting a suitable set of linearly independent vectors, a 1, a 2, … a n from B, the mineral composition, x, is easily computed from: x = E −1 b where E −1 is the inverse to some square array from A. This procedure of classification and computation is illustrated for the three mineral groups feldspar, biotite, and amphibole.