Generalised Matrix Notation

Equations (4.15) or (4.16) represent the fit of a straight line to a set of data pairs. These equations can be written in an expanded form  

Recall the colon ( ) notation as introduced in Chapter 2.1, Matrices, Vectors, Scalars. The first column of F, fi, contains m ones, while the second 

Equation (4.19) and its predecessors describe the special case for a polynomial of degree one. It is straightforward to generalise by adding any number of terms or columns in F and elements in a. 

The prototype application is the fitting of the np linear parameters, a, .a p defining a higher order polynomial of degree np-1. The generalisation of equation (4.5) reads as  

In matrix notation, the equivalent of equation (4.15) can be written in the following way  

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It is more efficient to use ai and 02 as parameters rather than intercept and slope. More importantly, in 4.2.3, Generalised Matrix Notation we will be able to extend the vector containing the a-values to any higher dimension. 

As demonstrated in eq. (1.9) for any reactant this relationship can be written in a more generalised form in matrix notation as... 

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