Related papers: Improvements on some partial trace inequalities fo…
About last 70s, Haynsworth [6] used a result of the Schur complement to refine a determinant inequality for positive definite matrices. Haynsworth's result was improved by Hartfiel [5]. We extend their result to a larger class of matrices,…
Yuan and Leng (2007) gave a generalization of Ky Fan's determinantal inequality, which is a celebrated refinement of the fundamental Brunn-Minkowski inequality $(\det (A+B))^{1/n} \ge (\det A)^{1/n} +(\det B)^{1/n}$, where $A$ and $B$ are…
Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
The main purpose of this paper is to englobe some new and known types of Hermitian block-matrices $M=\begin{pmatrix} A \& X\\ {X^*} \& B\end{pmatrix}$ satisfying or not the inequality $\|M\|\le \|A+B\|$ for all symmetric norms
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…
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
The definition of Choi matrices for linear maps on the n x n matrices is extended to factors, and the basic theorems for Choi matrices are proved in this general context.
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin, Ma…
The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential…
In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality…
Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly…
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
Let $A$ be a positive semidefinite matrix, block partitioned as $$ A=\twomat{B}{C}{C^*}{D}, $$ where $B$ and $D$ are square blocks. We prove the following inequalities for the Schatten $q$-norm $||.||_q$, which are sharp when the blocks are…
We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger…
We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,\tau})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from…
A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…
Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation…
In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constant trace matrix variable. We then demonstrate how this…