Related papers: Singular Value Inequalities related to PPT Blocks
In this report, we aim to exemplify concentration inequalities and provide easy to understand proofs for it. Our focus is on the inequalities which are helpful in the design and analysis of machine learning algorithms.
It was recently observed that the singular values of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm decay exponentially. This property was used to solve, with a higher efficiency, certain…
An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in…
Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
Equivalencies of many basic elementary inequalities are given
In this paper, we present various inequalities for generalized numerical radius of $2 \times 2$ block matrices for Schatten p-norm. Moreover, we give a refinement of the triangle inequality for the Schatten p-generalized numerical radius.
We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…
We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing…
An integral in the sense of principal value of a singular function or of product of singular functions can appear itself as a singular function in some range of values of integration parameters. In this case, if necessary subsequently to…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
Some inequalities for different types of convexity are established.
We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…
In this paper we explore inequalities between symmetric homogeneous polynomials of degree four of three real variables and three nonnegative real variables. The main theorems describe the cases in which the smallest possible coefficient is…
We study the Pareto frontier for two competing norms $\|\cdot\|_X$ and $\|\cdot\|_Y$ on a vector space. For a given vector $c$, the pareto frontier describes the possible values of $(\|a\|_X,\|b\|_Y)$ for a decomposition $c=a+b$. The…
The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In this paper, we consider the value distribution of the differential polynomials $f^2f^{(k)}-1$ where $k$ is a positive integer, and obtain some estimates only by the reduced counting function. Our result answers a question in (Some…
A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…