Related papers: Improvements on some partial trace inequalities fo…

We describe all inequalities among generalized diagonals in positive semi-definite matrices. These turn out to be governed by a simple partial order on the symmetric group. This provides an analogue of results of Drake, Gerrish, and…

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.

A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.

In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary.

This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmetric biquadratic forms, we establish a connection between the…

We translate inequalities and conjectures for immanants and generalized matrix functions into inequalities in the L\"owner order. These have the form of trace polynomials and generalize the inequalities from [FH, J. Math. Phys. 62 (2021),…

We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively.…

We describe recent work of Kim in arXiv:1210.5190 to show that operator convex functions associated with quasi-entropies can be used to prove a large class of new matrix inequalities in the tri-partite and bi-partite setting by taking a…

Utilizing the notion of positive multilinear mappings, we give some matrix inequalities. In particular, Choi--Davis--Jensen and Kantorovich type inequalities including positive multilinear mappings are presented.

In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In…

We present an Oppenheim type determinantal inequality for positive definite block matrices. Recently, Lin [Linear Algebra Appl. 452 (2014) 1--6] proved a remarkable extension of Oppenheim type inequality for block matrices, which solved a…

We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…

We investigate the notion of partial trace ideals, recently introduced by Maitra. We first establish several properties of partial trace ideals and give affirmative answers to questions posed by Maitra. We then study the invariant defined…

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.

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the…

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…

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.…

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…