Related papers: Positive linear maps and eigenvalue estimates for …

We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

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.

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.

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

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.

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.

In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices…

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…

Eigenvalues inequalities involving (log) convex/concav functions and Hermitian matrices, positive unital maps are considered. Simple proofs of Bhatia-Kittaneh inequality and Naimark dilation theorem are given.

The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.

We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover the case of some positive linear maps on a von Neumann algebra mapping any nonzero operator to an unbounded…

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…

We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…

We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…