𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The statistics of the eigenvalues of random matrices

✍ Scribed by F. Cristofori; P.G. Sona; F. Tonolini

Publisher
Elsevier Science
Year
1966
Weight
212 KB
Volume
78
Category
Article
ISSN
0029-5582

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Tracy–Widom statistic for the largest ei
Tracy–Widom statistic for the largest eigenvalue of autoscaled real matrices
✍ Edoardo Saccenti; Age K. Smilde; Johan A. Westerhuis; Margriet M. W. B. Hendriks πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 297 KB

Eigenanalysis is common practice in biostatistics, and the largest eigenvalue of a data set contains valuable information about the data. However, to make inferences about the size of the largest eigenvalue, its distribution must be known. Johnstone's theorem states that the largest eigenvalues l 1

Strong Convergence of the Empirical Dist
Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices
✍ J.W. Silverstein πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 267 KB

Let \(X\) be \(n \times N\) containing i.i.d. complex entries with \(\mathbf{E}\left|X_{11}-\mathbf{E} X_{11}\right|^{2}=1\), and \(T\) an \(n \times n\) random Hermitian nonnegative definite, independent of \(X\). Assume, almost surely, as \(n \rightarrow \infty\), the empirical distribution functi

On the Empirical Distribution of Eigenva
On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices
✍ J.W. Silverstein; Z.D. Bai πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 500 KB

A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form \(A+X T X^{*}\), originally studied in Marcenko and Pastur, is presented. Here, \(X(N \times n), T(n \times n)\), and \(A(N \times N)\) are independent, with \(X\) containing i.i.d. entries hav