Related papers: Note on Bounds for Eigenvalues using Traces

We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.

In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.

For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.

We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.

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…

It is known (see e.g. [2], [4], [5], [6]) that continuous variations in the entries of a complex square matrix induce continuous variations in its eigenvalues. If such a variation arises from one real parameter $\alpha \in [0, 1]$, then the…

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.

We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues…

We give inequalities relating the eigenvalues of the adjacency matrix and the Laplacian of a graph, and its minimum and maximum degrees. The results are applied to derive new conditions for quasi-randomness of graphs.

We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the…

In this study, we found a regular trace formula for the eigenvalues of the boundary value problem, which we created with the second-order differential equation with eigen parameter and discontinuity at x ={\pi}/2, which is an interior point…

A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument…

We present sharp inequalities relating the number of vertices, edges, and triangles of a graph to the smallest eigenvalue of its adjacency matrix and the largest eigenvalue of its Laplacian.

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…

We consider path-connected sets of matrices and the induced paths between eigenvalues. We discuss the equivalence relation generated by these paths, and how it relates to the presence of higher multiplicity eigenvalues realized by the set.…

We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest…

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…

This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…