线性映射的零空间与值域的若干性质

On the Properties of Null-space and Range Space of Linear Mappings

本文讨论了数域F上向量空间上线性映射的零空间和值域的一些性质,证明了秩与零度定理,并研究了n维向量空间V上的两个线性变换的零空间和值域之间的关系。

Properties on the null-space and range space of linear mappings which defined on the vector space on numerical field F are discussed in this paper;the rank and nullity theorem is to be proved.And at the same time,the relation between null-space and range space of two linear transforms is also investigated.