Condition number of a square matrix with i.i.d. columns drawn from a convex body

DOI10.1090/S0002-9939-2011-10994-8zbMath1244.15024OpenAlexW1986387405MaRDI QIDQ2880660

Alain Pajor, Olivier Guédon, Nicole Tomczak-Jaegermann, Radosław Adamczak, Alexander E. Litvak

Publication date: 13 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10994-8

zbMATH Keywords

normcondition numberconvex bodieslog-concave distributionsisotopic distributionssmallest single valuesquare random matrices

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Probabilistic methods in Banach space theory (46B09) Random matrices (algebraic aspects) (15B52) Conditioning of matrices (15A12) Asymptotic theory of Banach spaces (46B06)

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Cites Work

• Unnamed Item
• Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling
• Concentration of mass on convex bodies
• Smallest singular value of random matrices with independent columns
• Condition numbers of random matrices
• Convex measures on locally convex spaces
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Volume estimates for log-concave densities with application to iterated convolutions
• Invertibility of random matrices: norm of the inverse
• Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
• The Littlewood-Offord problem and invertibility of random matrices
• Smallest singular value of random matrices and geometry of random polytopes
• On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• On the efficiency of algorithms of analysis
• Eigenvalues and Condition Numbers of Random Matrices
• Small ball probability estimates for log-concave measures