Smallest singular value of a random rectangular matrix

Smallest Singular Value of a Random Rectangular Matrix

We prove an optimal estimate of the smallest singular value of a random subGaussian matrix, valid for all dimensions. For an N n matrix A with independent and identically distributed sub-Gaussian entries, the smallest singular value of A is at least of the order p N pn 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc.

The Smallest Singular Value of a Random Rectangular Matrix

We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N × n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order √ N − √ n − 1 with high probability. A sharp estimate on the probability is also obtained.

The Smallest Singular Value of a Random Rectangular Matrix Mark Rudelson and Roman Vershynin

We prove an optimal estimate of the smallest singular value of a random subgaussian matrix, valid for all dimensions. For an N × n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order √ N − √ n − 1 with high probability. A sharp estimate on the probability is also obtained.

Loewner matrix ordering in estimation of the smallest singular value

Iterative Computation of the Smallest Singular Value and the Corresponding Singular Vectors of a Matrix

Technische Universit at Dresden Herausgeber: Der Rektor Iterative Computation of the Smallest Singular Value and the Corresponding Singular Vectors of a Matrix Hubert Schwetlick and Uwe Schnabel IOKOMO-06-97 December 1997 Preprint-Reihe IOKOMO der DFG-Forschergruppe Identi kation und Optimierung komplexer Modelle auf der Basis analytischer Sensitivitatsberechnungen an der Technischen Universi...