Related papers: Problems and Conjectures in Matrix and Operator In…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…
The inverse of the Vandermonde and confluent Vandermonde matrices are presented. In the case of the Vandermonde matrix, we present a decomposition in three factors, one of them a diagonal matrix. The evaluation of such inverse matrices is a…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
A yet unmet challenge in algorithmic fairness is the problem of intersectionality, that is, achieving fairness across the intersection of multiple groups -- and verifying that such fairness has been attained. Because intersectional groups…
One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
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 paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
In this article, we employ certain properties of the transform $C_{M,m}(A)=(MI-A^*)(A-mI)$ to obtain new inequalities for the bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. In particular, we obtain new relations among…
Inequalities play important roles not only in mathematics, but also in other fields, such as economics and engineering. Even though many results are published on Hermite-Hadamard (H-H) type inequalities, new researcher to this fields often…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…
We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…
In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles given by the previous functions…