Related papers: Computations on Some Hankel Matrices
In this paper, we obtain the sharp bounds of the second Hankel determinant of logarithmic inverse coefficients for the starlike and convex functions.
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
We derive tight lower bounds on the smallest eigenvalue of a sample covariance matrix of a centred isotropic random vector under weak or no assumptions on its components.
We investigate the large $N$ behavior of the smallest eigenvalue, $\lambda_{N}$, of an $\left(N+1\right)\times \left(N+1\right)$ Hankel (or moments) matrix $\mathcal{H}_{N}$, generated by the weight…
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
In this paper we investigate the smallest eigenvalue, denoted as $\la_N,$ of a $(N+1)\times (N+1)$ Hankel or moments matrix, associated with the weight, $w(x)=\exp(-x^{\bt}),x>0,\bt>0$, in the large $N$ limit. Using a previous result, the…
We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with…
We consider the $n\times n$ Hankel matrix $H$ whose entries are defined by $H_{ij}=1/s_{i+j}$ where $s_k=(k-1)!$ and prove that $H$ is invertible for all $n\in\mathbb{N}$ by providing an explicit formula for its inverse matrix.
In this paper, we obtain the upper bounds to the third Hankel determinants for starlike functions of order $\alpha$, convex functions of order $\alpha$ and bounded turning functions of order $\alpha$. Furthermore, several relevant results…
In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…
In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…
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…
In this paper, we obtain two new lower bounds for the smallest singular value of nonsingular matrices which is better than the bound presented by zou \cite{zou2012lower}, Lin, Minghua and Xie, Mengyan \cite{lin2021some} under certain…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
In this paper we express the eigenvalues of anti-heptadiagonal persymmetric Hankel matrices as the zeros of explicit polynomials giving also a representation of its eigenvectors. We present also an expression depending on localizable…
In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are…
The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.
Let ${\mathcal A}$ be the class of functions that are analytic in the unit disc ${\mathbb D}$, normalized such that $f(z)=z+\sum_{n=2}^\infty a_nz^n$, and let class ${\mathcal U}(\lambda)$, $0<\lambda\le1$, consists of functions…
In this note, we demonstrate a method to invert some Hankel matrices explicitly by using the kernel polynomials for the related classical orthogonal polynomials.