Related papers: Trace inequalities for products of matrices

We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.

The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a…

We prove boundary inequalities in arbitrary bounded Lipschitz domains on the trace space of Sobolev spaces. For that, we make use of the trace operator, its Moore-Penrose inverse, and of a special inner product. We show that our trace…

Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization

This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…

We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.

For two matrices $A$ and $B$, and large $n$, we show that most products of $n$ factors of $e^{A/n}$ and $n$ factors of $e^{B/n}$ are close to $e^{A + B}$. This extends the Lie-Trotter formula. The elementary proof is based on the relation…

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…

One may identify the general properties of the neutrino mass matrix by generating many random mass matrices and testing them against the results of the neutrino experiments.

Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…

The standard approach for computing the trace of the inverse of a very large, sparse matrix $A$ is to view the trace as the mean value of matrix quadratures, and use the Monte Carlo algorithm to estimate it. This approach is heavily used in…

We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…

We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…

In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…

Equivalencies of many basic elementary inequalities are given

This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.

In this article we propose a general method of obtaining infinite sums of products with functions that count patterns in numbers.

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and…