UC知道帮忙翻译一下，这个是论文摘要，要尽量学术、准确一些，谢谢了！
来源：百度知道 编辑：UC知道 时间：2024/06/06 08:19:05
等价分类思想在各门学科的研究中都有着重要的作用，利用等价分类可以将复杂的事物分类并取出每一类的代表元进行研究，从而简化研究。本文介绍了等价关系在数学中的含义以及性质，并从高等代数、抽象代数、拓扑方面列举了矩阵的相抵、相似、合同；向量组的等价、线性空间的同构；群的陪集、同构；环的理想、同构以及拓扑中的同胚等几种等价关系在数学中的常见应用。
有可能用到的单词：等价分类Equivalent classification 高等代数higher algebra 抽象代数abstract algebra 拓扑topology 矩阵matrix 相似similitude 合同congruent 向量vector 线性空间linear space 同构somorphism 陪集coset 理想 ideal 拓扑同胚topological homeomorphism
有可能用到的单词：等价分类Equivalent classification 高等代数higher algebra 抽象代数abstract algebra 拓扑topology 矩阵matrix 相似similitude 合同congruent 向量vector 线性空间linear space 同构somorphism 陪集coset 理想 ideal 拓扑同胚topological homeomorphism
供您参考
Equivalent Classification(EC) plays an important role in studying many subjects,we could classify the complicated things by means of EC and get the typical model from them so that we can simplify the study.
Firstly,It introduces the definition and character of EC used in Math. Secondly,it enumerates similitude and congruent of Matrix, equivalent of Vectors, somorphism of Linear space in terms of Higher Algebra, Abstract Algebra and Topology.Finally, it explains the frequent applications of EC in Math, for example, the coset and somorphism of Group, the ideal and somorphism of Ring, the topological homeomorhpism, etc..