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CONDITION NUMBER OF A SQUARE MATRIX WITH I.I.D. COLUMNS DRAWN FROM A CONVEX BODY.
- Source :
- Proceedings of the American Mathematical Society; Mar2012, Vol. 140 Issue 3, p987-998, 12p
- Publication Year :
- 2012
-
Abstract
- We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic log-concave distribution. An important example is obtained by sampling vectors uniformly distributed in an isotropic convex body. We deduce that the condition number of such matrices is of the order of the size of the matrix and give an estimate on its tail behaviour. [ABSTRACT FROM AUTHOR]
- Subjects :
- RANDOM matrices
CONVEX bodies
CONVEX functions
LOGARITHMS
GEOMETRIC analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 140
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 67434879
- Full Text :
- https://doi.org/10.1090/S0002-9939-2011-10994-8