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The method of perpendiculars of finding estimates from below for minimal singular eigenvalues of random matrices. (English) Zbl 1390.15029

Summary: 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.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B52 Random matrices (algebraic aspects)
15B51 Stochastic matrices
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