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

DOI10.1515/rose-2018-0009zbMath1390.15029OpenAlexW2805798108MaRDI QIDQ1635517

Vyacheslav L. Girko

Publication date: 6 June 2018

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/rose-2018-0009

zbMATH Keywords

eigenvaluesrandom matrixcanonical equations

Mathematics Subject Classification ID

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

Related Items

The limit \(G\)-law for the solutions of systems of linear algebraic equations with independent random coefficients under the \(G\)-Lindeberg condition ⋮ The respect method. Simple proof of finding estimates from below for minimal singular eigenvalues of random matrices whose entries have zero means and bounded variances

Cites Work

• Unnamed Item
• Unnamed Item
• How close is the sample covariance matrix to the actual covariance matrix?
• Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
• The Littlewood-Offord problem and invertibility of random matrices
• Smallest singular value of random matrices and geometry of random polytopes
• Sharp lower bounds on the least singular value of a random matrix without the fourth moment condition
• The smallest singular value of random rectangular matrices with no moment assumptions on entries
• Condition number of a square matrix with i.i.d. columns drawn from a convex body
• Non-asymptotic theory of random matrices: extreme singular values
• Smooth analysis of the condition number and the least singular value
• Bounding the Smallest Singular Value of a Random Matrix Without Concentration
• Smallest singular value of a random rectangular matrix
• 35 years of the Inverse Tangent Law
• The Circular Law. Thirty years later