Classical Least Squares K-Matrix

The classical least squares (CLS) approach is based on the representation of Beer s law in matrix form [5], Consider the simplest case of a two-component system. Owing to the additive nature of Beer s law, the following equations can be written as follows (equations (14) and (15))  

These equations can be rewritten in matrix form (equation (16) as  

The calibration step in the CLS approach then involves the determination of the elements of the K matrix using the spectral data for a series of cahbration standards. For an n-component analysis, this involves the solution of a matrix equation of the form given in equation (18)  

The major limitation of the CLS technique becomes apparent if we consider the form of equations (14) and (15). In this two-component case, the 

In the inverse least squares (ILS) approach [6], the matrix equation expressing Beer s law is rearranged into equation (19)  

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