Quantitative invertibility of non-Hermitian random matrices
Konstantin Tikhomirov
TL;DR
This paper reviews recent advances in understanding the invertibility of non-Hermitian random matrices, focusing on estimating their smallest singular values and exploring related applications.
Contribution
It provides a comprehensive survey of recent methods and results in the quantitative invertibility of non-Hermitian random matrices, highlighting new theoretical insights.
Findings
Improved bounds on smallest singular values
Applications to spectral distribution analysis
Connections to matrix computation stability
Abstract
The problem of estimating the smallest singular value of random square matrices is important in connection with matrix computations and analysis of the spectral distribution. In this survey, we consider recent developments in the study of quantitative invertibility in the non-Hermitian setting, and review some applications of this line of research.
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Taxonomy
TopicsRandom Matrices and Applications · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics