Der Richtungsabstand. (The direction distance) (Q1802856)

The author introduces the concept of a distance between directions (for a nonzero vector \(z\) in a vector space over \(\mathbb{R}\), its direction is defined as \([z]:=\{\mu z|\mu\in\mathbb{R}_{>0}\}\), its unit vector as \(z_ 0:=z/| z|\), and the distance between two directions \([x]\) and \([y]\) is defined to be the function \(d[x/y]\) defined on \(\mathbb{R}_{>0}\times\mathbb{R}_{>0}\) by \(d[x/y](\alpha,\beta):=|\alpha x_ 0-\beta y_ 0|)\), studies its properties and discusses its relevance to statistics.