Lower eigenvalue bounds for 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...

Analysis of Eigenvalue Bounds for Real Symmetric Interval Matrices

In this paper, we present several verifiable conditions for eigenvalue intervals of real symmetric interval matrices overlapping or not overlapping. To above cases, two new methods with algorithms for computing eigenvalue bounds of real symmetric matrices are developed. We can estimate eigenvalue bounds moving away the assumption that two intervals containing two eigenvalues of real symmetric i...

Lower Bounds for Some Factorable Matrices

The following conjecture was posed by Axler and Shields. Let {xn} be a monotone decreasing sequence of nonnegative numbers, C the Cesáro matrix of order one. What is the best constant K for which ‖Cx‖2 ≥ K‖x‖2 for all such sequences {xn}? Lyons [3] determined that the best constant is π/ √ 6. This result was extended to p spaces for p > 1 by Bennett [1]. In [1], Bennett established the followin...