Related papers: Some matrix inequalities of log-majorization type
We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain…
The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In…
The aim of this paper is to study the logarithmic submajorisations inequalities for operators in a finite von Neumann algebra. Firstly, some logarithmic submajorisations inequalities due to Garg and Aulja are extended to the case of…
In this paper, Hermite-Hadamard type inequality for Sugeno integrals based on log-convex functions is studied. Some examples are given to illustrate the results.
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
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.
The aim of this paper is to discuss various concentration inequalities for U-statistics and most recent results. A special focus will be on providing proofs for bounds on the U-statistics using classical concentration inequalities, which,…
The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is…
We derive the loop equation for the 1-matrix model with generic difference-type measure for eigenvalues and develop a recursive algebraic framework for solving it to an arbitrary order in the coupling constant in and beyond the planar…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq…
A generalized eigenvector of a hypermatrix, called the universal (U-) eigenvector, is proposed, which extended the notion of diagonal (D-) eigenvectors in the literature. Using the semi-tensor product, the homogeneous U-eigenequation can be…
We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to…
Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Greene--Skandera (2011), Sra (2016), Khare--Tao (2021),…
We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$…
In this paper, the authors establish a new type integral inequalities for differentiable s-convex functions in the second sense. By the well-known H\"older inequality and power mean inequality, they obtain some integral inequalities related…
We show that the unitary factor U in the polar decomposition of a nonsingular matrix Z = U H is the minimizer for both ||Log(Q^* Z)|| and ||sym (Log(Q^*Z))|| over unitary Q, for any given invertible complex n-times-n matrix Z, for any…
In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral…
The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.