ABSTRACT
The intuitive appreciation of linear algebra is greatly aided by a geometrical interpretation in which vectors are represented by points and matrices are regarded as representations of linear transformations or functions. This chapter discusses some stronger justification of the method is really desirable and such a justification is provided by the celebrated theorem. Determination of a least-squares estimate is not a difficult problem. The method of least squares has been introduced on the purely intuitive basis that if we estimate the mean of a distribution by the parameter nearest the observation made, this estimate should be quite good, since the observation is probably near the true mean. The algebra of the Gauss–Markov theorem suggests the appropriate modification to the method of least squares when either the errors have different variances or when they are correlated.
