\"{U}ber die Winkel zwischen Unterr\"{a}ume

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.