ADDENDUM PROOF OF EQS. 7.1-16 AND

The following identities for real nonsingular matrices X and B are derived by Bard (1974)  

Here the elements of dX are treated as independent. The matrix X of interest here is. the inverse covariance matrix of response block b. Elements of X are marked with superscript indices, and (X) is the transpose of X. 

Solving for p 6. S 6) Y) then gives Eq. (7.1-16), and maximization of the latter function over 6 gives the modal parameter vectoi 0, valid equally for Eqs. (7.1-16) and (7.1-14). Application of Eq. (A.6) at 6 yields Eq. (7.1-17) as the modal estimate of the covariance matrix. 

Modify Example C.4 of Appendix C to do the parameter estimation on the assumption of a diagonal S matrix. To do this, set the number of blocks NBLK equal to the number of responses and the block widths IBLK(K.l) equal to 1. Then do the following calculations  

Modify Example C.4 to use the array OBS directly, ignoring the mass-balance condition i yiu.adj = 1- The full set of experimental data is given in the table below  

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