We will also compare two different traditions where the linear model is applied: The first is the classical one of applications in physical sciences, in particular astronomy and geodesy. It starts with the least squares method of Gauss and Legendre and it culminates in the statistical justification of the choice of weight matrix as a scalar multiple of the inverse of the error covariance matrix. According to the celebrated Gauss-Markov theorem with this choice the least squares solution provides Best Linear Uniformly Unbiased Estimates (BLUUE or simply BLUE) for all linear functions of the parameters, which are estimable, i.e. functions of the observables only.
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