Euclidean Distance between Two Linear Varieties

2013/12/16 by Vicente, M. A. Facas, Gonçalves, Armando, Vitória, José
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1312.4406

Abstract

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.

Related

• The Euclidean Distance Degree of Orthogonally Invariant Matrix Varieties
• The Euclidean distance degree of an algebraic variety
• Optimal Pair of Two Linear Varieties
• The Euclidean distance degree of curves: from rational to line multiview varieties
• Conditional Euclidean distance optimization via relative tangency