Statistics – Computation
Scientific paper
Jun 1967
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1967gecoa..31.1043p&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 31, Issue 6, pp.1043-1078
Statistics
Computation
2
Scientific paper
The conservation of mass within any mineral that is regarded as a closed system is expressed by the equations: 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.
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