The smallest singular value of inhomogeneous square random matrices
The smallest singular value of inhomogeneous square random matrices
We show that, for an n×n random matrix A with independent uniformly anticoncentrated entries such that E‖A‖HS2≤Kn2, the smallest singular value σn(A) of A satisfies P{σn(A)≤ε n}≤Cε+2e−cn,ε≥0. This extends earlier results (Adv. Math. 218 (2008) 600–633; Israel J. Math. 227 (2018) 507–544) by removing the assumption of mean zero and …