Über die Winkel zwischen Unterräumen
Volume 162 / 2020
Colloquium Mathematicum 162 (2020), 143-157
MSC: Primary 11J13.
DOI: 10.4064/cm7885-7-2019
Published online: 27 April 2020
Abstract
We prove a metric statement about approximation of an $n$-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.
