The method of perpendiculars of finding estimates from below for minimal singular eigenvalues of random matrices

摘要

The lower bounds for the minimal singular eigenvalue of the matrix are obtained under the G-Lindeberg condition and the G-double stochastic condition for the variances of the matrix entries. The new method is based on the G-method of perpendiculars, the REFORM method, the martingale method, and the theory of canonical spectral equations.