相关论文: Numerical Radius of Products of Special Matrices
The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
In this paper, we investigate the generalized numerical radius $\omega_N$, associated with a matrix norm $N$ defined by $\omega_N(X) = \sup_{\theta \in \mathbb{R}} N(\operatorname{Re}(e^{i\theta}X))$. We focus on matrices whose numerical…
We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…
In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral…
In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are…
We prove an inequality for the spectral radius of products of non-negative matrices conjectured by X. Zhan. We show that for all $n\times n$ non-negative matrices $A$ and $B$, $\rho(A\circ B)\le\rho((A\circ A)(B\circ B))^{1/2}\le\rho(AB)$,…
If $A$ and $B$ are nonnegative matrices, a sharp upper bound on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices is given, and the minimum eigenvalue $\tau(A\star B)$ of the Fan product of two…
We introduce numerical characteristics of Sylvester and Hadamard matrices and give their estimates and some of their applications.
We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the results obtained we give a better estimation for the zeros of a…
A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower…
A presentation of numerical range for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Then we are extended to the treatment of rank-k numerical range.
We obtain several upper and lower bounds for the numerical radius of sectorial matrices. We also develop several numerical radius inequalities of the sum, product and commutator of sectorial matrices. The inequalities obtained here are…
In this work, some generalizations and refinements inequalities for numerical radius of the product of Hilbert space operators are proved. New inequalities for numerical radius of block matrices of Hilbert space operators are also…
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…