Properties of matrices

The layout of the thesis: In addition to the introduction, conclusion, list of symbols and abbreviations, list of tables, list of images and drawings, list of published works related to the thesis. Project, appendices and references.

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Let A be an n × n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A−1 does not exceed Cn3/2 with probability close to 1. 1. Introduction Let A be an n × n matrix, whose entries are independent, identically distributed random variables. The spectral properties of such matrices, in particular invertibility, have been extensively studied (see, e.g. [M] and the survey [DS]).

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