Related papers: A matrix trace inequality and its application
Nonlinear matrix equations play a crucial role in science and engineering problems. However, solutions of nonlinear matrix equations cannot, in general, be given analytically. One standard way of solving nonlinear matrix equations is to…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
In this paper we present some reverses of the Golden-Thompson type inequalities: Let $H$ and $K$ be Hermitian matrices such that $ e^s e^H \preceq_{ols} e^K \preceq_{ols} e^t e^H$ for some scalars $s \leq t$, and $\alpha \in [0 , 1]$. Then…
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…
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the…
We study the trace set of the commutator subgroup of $\Gamma(2),$ a type of Local-Global problem about thin groups. We determine the local obstructions and then use the correspondence between binary quadratic forms and hyperbolic matrices…
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…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.
The aim of this note is to show that certain number theoretic inequalities due to Nesbitt and Shapiro have noncommutative counterparts involving positive definite matrices.
In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
In this paper we obtain some existence result of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence,…
We determine when a matrix is similar to a partial isometry, refining a result of Halmos--McLaughlin.
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…