Related papers: Characterization of vector spaces by isomorphisms

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…

In this talk I will introduces two spaces: the first space is the usual n-dimensional vector space with the unusual feature that n is non-integer, the second space is composed by the linear matrices acting on the previous space (physicists…

Word embeddings are rich word representations, which in combination with deep neural networks, lead to large performance gains for many NLP tasks. However, word embeddings are represented by dense, real-valued vectors and they are therefore…

A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and Paul for real scalars. In this paper, we give a different…

The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…

Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…

We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere…

Given vector representations for individual words, it is necessary to compute vector representations of sentences for many applications in a compositional manner, often using artificial neural networks. Relatively little work has explored…

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated…

With this paper, we gain a better understanding of the set of near-field structures on a fixed scalar group. If we were able to describe all near-field structures on a fixed scalar group, we could describe all near-vector spaces. The…

We derive generic equations for a vector field driving the evolution of flat homogeneous isotropic universe and give a comparison with a scalar filed dynamics in the cosmology. Two exact solutions are shown as examples, which can serve to…

Neural network models often face challenges when processing very small or very large numbers due to issues such as overflow, underflow, and unstable output variations. To mitigate these problems, we propose using embedding vectors for…

We generalize the notion of S-equivalence, previously defined for semistable vector bundles, to points in arbitrary algebraic stacks and use it to describe the identification of points when passing to the moduli space. As applications, we…

We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…

Vector-space models, from word embeddings to neural network parsers, have many advantages for NLP. But how to generalise from fixed-length word vectors to a vector space for arbitrary linguistic structures is still unclear. In this paper we…