Related papers: A matrix trace inequality and its application

A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.

This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…

With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions…

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.

Newton's inequalities $c_n^2 \ge c_{n-1}c_{n+1}$ are shown to hold for the normalized coefficients $c_n$ of the characteristic polynomial of any $M$- or inverse $M$-matrix. They are derived by establishing first an auxiliary set of…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms on $m$ orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the paper…

The matrix version of the entropy-power inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.

We give an elementary estimate that entails and generalises numerous Korn inequalities scattered in the literature. As special instances, we obtain general Korn-type inequalities involving normal or tangential trace components, or lower…

We investigate the relationship between partial traces and their dilations for general complex matrices, focusing on two main aspects: the existence of (joint) dilations and norm inequalities relating partial traces and their dilations.…

Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von…

Jensen's trace inequality is established for every multivariable, convex function and every trace or trace-like functional on a C*-algebra.

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…

In this short paper, we show a certain matrix trace inequality and then give a refinement of the trace inequality proven by Belmega, Lasaulce and Debbah. In addition, we give an another improvement of their trace inequality.

The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely $\rank(\sum^K_{j=1} A_j^T \otimes B_j)\le K \cdot…

A mapping M(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection…

We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application we reprove and extend some theorems about eigenvalue asymptotics of Schr\"odinger operators with homogeneous potentials. The…

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.

Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo trace inequality. At the endpoint they satisfy a…

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…

We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are…