On Multi-Vector Spaces

向量空间的参数理论及其在模糊向量空间中的应用

A Parametric Theory of Vector Spaces with Applications to Fuzzy Vector Spaces

提出向量空间参数化框架，每个向量由依赖参数的实现表示，应用于模糊向量空间。

强正则近向量空间的内积与有限维近向量空间的对偶性

Inner products for strongly regular near-vector spaces and duality for finite dimensional near-vector spaces

本文构建有限维近向量空间的对偶理论，为强正则近向量空间引入适配内积，拓展经典内积框架，同时将广义加权均值理论推广至任意复数据集。

Algebraic Vector Spaces

We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the problems that the language established here can inspire.

Some results on multi vector space

In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.

Reflexivity of a Banach Space with a Countable Vector Space Basis

All most all the function spaces over real or complex domains and spaces of sequences, that arise in practice as examples of normed complete linear spaces (Banach spaces), are reflexive. These Banach spaces are dual to their respective spaces of continuous linear functionals over the corresponding Banach spaces. For each of these Banach spaces, a countable vector space basis exists, which is responsible for their reflexivity. In this paper, a specific criterion for reflexivity of a Banach space with a countable vector space basis is presented.

非交换代数中的协变性

Covariance in Non-Commutative Algebra

本文在非交换可除代数上的向量空间中，通过群 $GL$ 在基流形上的主动与被动表示，研究被动变换如何诱导坐标变换，并基于协变性原理分析几何对象及多重线性映射的坐标变换性质。