仿射集与极大仿射无关组

Affine Sets and Maxinal Affinely Independent Quantities

在为了便于认识和描述仿射集的结构以及仿射集的其它性质 ,根据仿射无关的定义 ,本文提出了极大仿射无关组的概念 ,并给出了平凡与非平凡的仿射集中极大仿射无关组与极大线性无关组的关系。其中许多关系是线性关系 ,所以它们比较深刻彻底地反映了仿射集与极大仿射无关组的本质特征与内在联系。

In order to learn and describe affine sets' structure and their other properties,the concept of maximal affinely independent quantities is proposed through the definition of affine independence,in addition,the relations between maximal affinely independent quantities and maximal linearly independent quantities in trival affine sets and non-trival affine sets are studied respectively in this paper.Because some of the relations given here are equivalent relations,they show the main characters of affine sets,maximal affinely independent quantities and their inherent relationship deeply and thoughly.