Symmetric adjustment matrix

The simplest way to get a symmetric adjustment matrix Q that satisfies (3.143) is... 

When normal co-ordinates, defined by equations (1.13), are employed, it is possible to make use of the arbitrariness of the transform matrix to define matrix Q in such a way that matrix B in the right-hand side of equation (2.16) assumes a diagonal form after transformation. The problem of the simultaneous adjustment of the symmetrical matrices A and B to a diagonal form does have a solution. Since matrix A is defined non-negatively and B is defined positively, it is possible to find a transformation such that B is transformed into a unit matrix (with accuracy to constant multiplier), and A into a diagonal matrix. Therefore, one can write simultaneously the equations... 

The adjustment of the symmetric function to the energy flows from wood carbonization is an original and dynamic (and no more static) approach. The analysis of the symmetric logistic function demonstrates again the dramatic effect of water. As for mass flows, energy flows are delayed and slowed down for wet wood samples (H37). Water intervenes through the large quantities of heat it requires to he evaporated and eliminated from the solid matrix. 

With more than two variables the L terms are simply expanded to include more terms. For a two-parameter equation the size of the matrix remains 2. For a six-parameter equation with two variables, the size of the matrix is a symmetrical 6x6. Thus, only 27 sums need be calculated. The 6x6 square matrix is inverted and multiplied by the 1x6 matrix to obtain corrections in the six parameters. These are then adjusted and the process iterated to convergence. The iteration is controlled with a Visual Basic Macro. The rigorous inclusion of estimates for parameters from other experiments is easily incorporated into this procedure. The parameters and errors must be input. Next the program simply adds terms to the appropriate sums. For example, if the value of a has been determined to be ax with an uncertainty of sa, then the quantity 1 / (sa sa) is added to [a a ] and this quantity is multiplied by (aest —ax) and added to /-oa ] The adjustment is made as before, as are the parameters and uncertainties obtained. This has been demonstrated by Wentworth, Hirsch, and Chen [Chapt. 5, 37],... 

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