Controlling the least eigenvalue of a random Gram matrix
نویسندگان
چکیده
منابع مشابه
A Statistical Mechanics Analysis of Gram Matrix Eigenvalue Spectra
The Gram matrix plays a central role in many kernel methods. Knowledge about the distribution of eigenvalues of the Gram matrix is useful for developing appropriate model selection methods for kernel PCA. We use methods adapted from the statistical physics of classical fluids in order to study the averaged spectrum of the Gram matrix. We focus in particular on a variational mean-field theory an...
متن کاملEigenvalue Separation in Some Random Matrix Models
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/(2N)1/2, where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secul...
متن کاملThe Least Eigenvalue of Graphs
In this paper we investigate the least eigenvalue of a graph whose complement is connected, and present a lower bound for the least eigenvalue of such graph. We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
متن کاملThe Empirical Eigenvalue Distribution of a Gram Matrix: from Independence to Stationarity∗
1 Supélec (Ecole Supérieure d’Electricité), Plateau de Moulon, 3, rue Joliot-Curie, 91192 Gif Sur Yvette Cedex, France. E-mail: [email protected] 2 IGM LabInfo, UMR 8049, Institut Gaspard Monge, Université de Marne La Vallée, 5, Bd Descartes, Champs sur Marne, 77454 Marne La Vallée Cedex 2, France. E-mail: [email protected] 3 CNRS, Télécom Paris 46, rue Barrault, 75013 Paris, France. E...
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.048