Related papers: Hyperinner product spaces
Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…
We introduce a novel latent vector space model that jointly learns the latent representations of words, e-commerce products and a mapping between the two without the need for explicit annotations. The power of the model lies in its ability…
In this paper, we analyze the definition Andr\'e proposed for near-vector spaces to make it more transparent. We also study the class of near-vector spaces over division rings and give a characterization of regularity that gives a new…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
We propose a notion of weak (n+k,n)-category, which we call (n+k,n)-Theta-spaces. The (n+k,n)-Theta-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal's…
I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible…
Given the Hilbert space compression of two groups, we find bounds on the Hilbert space compression of their free product. We also investigate the Hilbert space compression of an HNN-extension of a group relative to a finite normal subgroup…
A finite set X in the Euclidean space is called an s-inner product set if the set of the usual inner products of any two distinct points in X has size s. First, we give a special upper bound for the cardinality of an s-inner product set on…
By studying the warped(or weighted) area-minimizing hypersurface, we prove that the metric can be locally split as a warped product metric under the spectral Ricci or spectral scalar curvature lower bound condition.
An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of…
We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…
We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties take the form "certain functors preserve profinite coproducts".…
In our previous paper [9], we have introduced topological nearly entropy, Ent_N (f) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied. Furthermore, we…
This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
In this paper we introduce the hypo-q-norms on a Cartesian product of normed linear spaces. A representation of these norms in terms of bounded linear functionals of norm less than one, the equivalence with the q-norms on a Cartesian…
Embedding methods for product spaces are powerful techniques for low-distortion and low-dimensional representation of complex data structures. Here, we address the new problem of linear classification in product space forms -- products of…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…