caa a22 4500 465791913 CHVBK 20180323112027.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF00306408 doi (NATIONALLICENCE)springer-10.1007/BF00306408 Powell Roger Department of Geology, University of Melbourne, 3052, Parkville, Victoria, Australia aut Matrix analysis of metamorphic mineral assemblages and reactions: alternatives and extensions [Elektronische Daten] [Roger Powell] Fisher (1989) advocated using the Singular Value Decomposition (SVD) of the composition matrix of a set of minerals for the determination of reactions between the minerals, and therefore of the compatibility relationships between mineral assemblages. The advantage of using the SVD for this is that an independent set of reactions, the left nullspace of the composition matrix, can be determined for a rank-deficient composition matrix which is close to, or within error of, the observed matrix. The zero singular values in the SVD can be identified by propagating the measurement uncertainties through to the singular values, and saying that singular values are zero if they are within error of zero. Having obtained an independent set of reactions, the reactions in the independent set can be combined linearly to find the full set of reactions. Propagating the measurement uncertainties through to the left nullspace of the composition matrix, the uncertainties in the coefficients of the reactions in the independent set can be determined. From these uncertainties, the uncertainties in all of the reactions can be determined, allowing the identification of reactions which are degenerate within error. This is important because it allows the identification of ambiguities in the compatibility relationships between mineral assemblages. Springer-Verlag, 1990 Contributions to Mineralogy and Petrology Springer-Verlag 106/1(1990-12-01), 61-65 0010-7999 106:1<61 1990 106 410 https://doi.org/10.1007/BF00306408 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00306408 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Powell Roger Department of Geology, University of Melbourne, 3052, Parkville, Victoria, Australia aut NATIONALLICENCE 773 0- Contributions to Mineralogy and Petrology Springer-Verlag 106/1(1990-12-01), 61-65 0010-7999 106:1<61 1990 106 410 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer