Related papers: Matrix forms of immanant inequalities
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
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.
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.
Let $T$ be a tree on $n$ vertices with $q$-Laplacian $L_T^q$ and Laplacian matrix $L_T$. Let $GTS_n$ be the generalized tree shift poset on the set of unlabelled trees on $n$ vertices. Inequalities are known between coefficients of the…
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
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…
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results…
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…
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…
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces, and then provide a unified extension of the recent…
We prove a matrix trace inequality for completely monotone functions and for Bernstein functions. As special cases we obtain non-trivial trace inequalities for the power function x->x^q, which for certain values of q complement McCarthy's…
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…
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…
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…
Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…
This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of…