Related papers: On the eigenvalues of combined meet and join matri…
We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general…
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.
In this paper, we study the eigenvalues of the GCD matrix $(S_n)$ and the LCM matrix $[S_n]$ defined on $S_n=\{1,2,\ldots,n\}$. We present upper and lower bounds for the smallest and the largest eigenvalues of $(S_n)$ and $[S_n]$ in terms…
Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…
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.
In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set $S_n$ is meet closed, we give a sufficient and necessary condition for the positive definiteness of the matrix $(S_n)_f$. From…
We determine, for any n $\ge$ 1, the generalized eigenvalues of an n x n MAX matrix to the corresponding MIN matrix. We also show that a similar result holds for the generalized eigenvalues of an nxn LCM matrix to the corresponding GCD…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
An upper bound on operator norms of compound matrices is presented, and special cases that involve the $\ell_1$, $\ell_2$ and $\ell_\infty$ norms are investigated. The results are then used to obtain bounds on products of the largest or…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
A number $\lambda \in \mathbb C $ is called an {\it eigenvalue} of the matrix polynomial $P(z)$ if there exists a nonzero vector $x \in \mathbb C^n$ such that $P(\lambda)x = 0$. Note that each finite eigenvalue of $P(z)$ is a zero of the…
In this paper we study the structure and give bounds for the eigenvalues of the $n\times n$ matrix, which $ij$ entry is $(i,j)^\alpha[i,j]^\beta$, where $\alpha,\beta\in\Rset$, $(i,j)$ is the greatest common divisor of $i$ and $j$ and…
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…
We consider the set $\mathcal{M}_n(\mathbb{Z}; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to…