Functional Analysis
Smallest singular value of random matrices with independent columns
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 853-856.

We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic symmetric log-concave distribution. We prove a deviation inequality in terms of the isotropic constant of the distribution.

On étudie la plus petite valeur singulière d'une matrice carrée aléatoire dont les colonnes sont des vecteurs aléatoires i.i.d. suivant une loi à densité log-concave isotrope. On démontre une inégalité de déviation en fonction de la constante d'isotropie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.011
Adamczak, Radosław 1; Guédon, Olivier 2; Litvak, Alexander 3; Pajor, Alain 4; Tomczak-Jaegermann, Nicole 3

1 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
2 Université Pierre-et-Marie-Curie, Paris 6, Institut de mathématiques de Jussieu, 4, place Jussieu, 75005 Paris, France
3 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
4 Équipe d'analyse et mathématiques appliquées, Université Paris Est, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallee cedex 2, France
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Adamczak, Radosław; Guédon, Olivier; Litvak, Alexander; Pajor, Alain; Tomczak-Jaegermann, Nicole. Smallest singular value of random matrices with independent columns. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 853-856. doi : 10.1016/j.crma.2008.07.011. http://www.numdam.org/articles/10.1016/j.crma.2008.07.011/

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