Lower bounds for the smallest singular value of structured random matrices
Lower bounds for the smallest singular value of structured random matrices
We obtain lower tail estimates for the smallest singular value of random matrices with independent but nonidentically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[M=A\circ X+B=(a_{ij}\xi_{ij}+b_{ij}),\] where $X=(\xi_{ij})$ has i.i.d. centered entries of unit variance and $A$ and $B$ are fixed matrices. In …