Fitting Requirements and the Solution of Chemical Problems

An reaction matrix R fits an X 6e-matrixB if the matrixS- -ff =.E is a 5e-matrix. 

In particular, E must be a symmetric matrix with non-negative entries. Since the sum of s3nnmetric matrices is symmetric, the requirement that E = 5 -t-iR be a e-matrix reduces to for each negative entry — riy of R there must be positive entry iyy of B, such that = / + (— tf ) 0. With the 

In order to refer to chemical systems which are conceivably capable of existence at observable concentrations, some further restrictions must be imposed upon E (see Section B). 

The Je-matrices of aU EM(i4) of an FIEM( ) can be manufactured from the be-matrix B of any one of the EM( ) and the set F B) of all reaction matrices R which fit -B.8) The 5e-matrices of all EM(4) with T valence electrons correspond to points in Rs whose chemical distance from the origin is = 2.  

using the chemical metric, F B) is isometric with F E) and B is isometric with E. 

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