Lower eigenvalue bounds for singular pencils of matrices

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Eigenvalue variance bounds for covariance matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices [7] and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investi...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Lower Bounds for the Smallest Singular Value of Structured Random Matrices

We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider n× n matrices with complex entries of the form M = A ◦X +B = (aijξij + bij) where X = (ξij) has iid centered entries of unit variance and A and B are fixed matrices. In our main result we obtain polynomial bounds on the smallest si...

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.