On the angles between certain arithmetically defined subspaces of ${𝐂}^n$

Brooks, Robert. "On the angles between certain arithmetically defined subspaces of ${\bf C}^n$." Annales de l'institut Fourier 37.1 (1987): 175-185. <http://eudml.org/doc/74742>.

@article{Brooks1987,
abstract = {If $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ are two families of unitary bases for $\{\bf C\}^n$, and $\theta $ is a fixed number, let $V^n$ and $W^n$ be subspaces of $\{\bf C\}^n$ spanned by $[\theta \cdot n]$ vectors in $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ respectively. We study the angle between $V^n$ and $W^n$ as $n$ goes to infinity. We show that when $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ arise in certain arithmetically defined families, the angles between $V^n$ and $W^n$ may either tend to $0$ or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.},
author = {Brooks, Robert},
journal = {Annales de l'institut Fourier},
keywords = {eigenvalue; angle between subspaces; lower bounds},
language = {eng},
number = {1},
pages = {175-185},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the angles between certain arithmetically defined subspaces of $\{\bf C\}^n$},
url = {http://eudml.org/doc/74742},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Brooks, Robert
TI - On the angles between certain arithmetically defined subspaces of ${\bf C}^n$
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 1
SP - 175
EP - 185
AB - If $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ are two families of unitary bases for ${\bf C}^n$, and $\theta $ is a fixed number, let $V^n$ and $W^n$ be subspaces of ${\bf C}^n$ spanned by $[\theta \cdot n]$ vectors in $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ respectively. We study the angle between $V^n$ and $W^n$ as $n$ goes to infinity. We show that when $\lbrace v_i\rbrace $ and $\lbrace w_j\rbrace $ arise in certain arithmetically defined families, the angles between $V^n$ and $W^n$ may either tend to $0$ or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.
LA - eng
KW - eigenvalue; angle between subspaces; lower bounds
UR - http://eudml.org/doc/74742
ER -