arXiv subjects
Publications and source records attributed to Armando Gonçalves.
The optimal pair of two linear varieties is considered as a best approximation problem, namely the distance between a point and the difference set of two linear varieties. The Gram determinant allows to get the optimal pair in closed form.
This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimising a target function. We propose a novel approach: to use the Moore-Penrose generalised inverse of a matrix in order to find the Euclidean distance and, at the same time, going further by exhibiting the best approximation pair of points.