Über die Winkel zwischen Unterräumen

Abstract

We prove a metric statement about approximation of a $n$-dimensional linear subspace $A$ in ${\mathbb{R}}^d$ by $n$-dimensional rational subspaces. We consider the problem of finding a rational subspace $B$ of bounded height $H=H(B)$ for which the angle of inclination $\psi (A,B)$ is small in terms of $H$. In the simplest case $d=4,n=2$ we give a partial solution of a problem formulated by W.M. Schmidt in 1967.

in German, this version contains minor corrections