This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimizing a target function. We propose a novel approach: to use the Moore-Penrose generalized 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.

Let Vbeafinitedirnensional vector space over thefield F and $(x) E F[x]. Let a: V--t Vbe a linear operator. Let S, be the set consisting of the vectors whose minimal polynomial 1s 4(x), together withthezero ~ector. Wegive anecessary and sufficient condition for S, to be a subspace.

No abstract

Abstract. 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.

No abstract