On the angles between certain arithmetically defined subspaces of 𝐂 n
Annales de l'Institut Fourier, Volume 37 (1987) no. 1, p. 175-185

If {v i } and {w j } are two families of unitary bases for C n , and θ is a fixed number, let V n and W n be subspaces of C n spanned by [θ·n] vectors in {v i } and {w j } respectively. We study the angle between V n and W n as n goes to infinity. We show that when {v i } and {w j } 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.

Pour {v i } et {w j } deux familles de bases de C n , et θ un nombre fixe, nous considérons V n et W n deux sous-espaces engendrés par [θ·n] vecteurs de {v i } et {w j } respectivement. Nous étudions l’angle entre V n et W n quand n tend vers l’infini. Nous démontrons que, quand {v i } et {w j } sont présents dans certaines familles définies arithmétiquement, l’angle entre V n et W n peut soit tendre vers 0, soit être minoré par une constante strictement positive. Ce comportement dépend d’un problème de valeur propre associé.

@article{AIF_1987__37_1_175_0,
     author = {Brooks, Robert},
     title = {On the angles between certain arithmetically defined subspaces of ${\bf C}^n$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {37},
     number = {1},
     year = {1987},
     pages = {175-185},
     doi = {10.5802/aif.1081},
     mrnumber = {89h:11022},
     zbl = {0611.15003},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_1987__37_1_175_0}
}
Brooks, Robert. On the angles between certain arithmetically defined subspaces of ${\bf C}^n$. Annales de l'Institut Fourier, Volume 37 (1987) no. 1, pp. 175-185. doi : 10.5802/aif.1081. https://aif.centre-mersenne.org/item/AIF_1987__37_1_175_0/

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