Details

Autor(en) / Beteiligte

• Rudelson, Mark
• Vershynin, Roman

Titel

Smallest singular value of a random rectangular matrix

Ist Teil von

• Communications on pure and applied mathematics, 2009-12, Vol.62 (12), p.1707-1739

Ort / Verlag

Hoboken: Wiley Subscription Services, Inc., A Wiley Company

Erscheinungsjahr

2009

Quelle

Access via Wiley Online Library

Beschreibungen/Notizen

• We prove an optimal estimate of the smallest singular value of a random sub‐Gaussian 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 √N − √n − 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc.