The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations.

中文翻译：

---

组合向量空间作为一种新型的三运算代数

本文的目的是定义和研究复合向量空间作为一种三运算代数。在这方面，通过提出非平凡的例子，强调它们是向量空间的适当推广，并且它们的结构可以通过使用线性算子来表征。此外，还研究了有关基础、组成子空间和残差元素的一些相关性质。此外，还展示了如何使用双射线性算子赋予向量空间复合结构。最后，组合向量空间的更多属性与线性变换有关。