空间分解成循环子空间直和的两个定理的新证明  

New Proofs of Two Theorems for Decomposing a Linear Space Into Direct Sum of Invariant Cyclic Subspaces

作　　者：石生明 朱一心[1] SHI Sheng-ming;ZHU Yi-xin(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《数学的实践与认识》2021年第22期294-303,共10页Mathematics in Practice and Theory

摘　　要：找到一个新方法,直接由线性空间理论证明:线性空间可以分解成循环子空间的直和.通常这是通过主理想整环上的有限生成模理论证明的.This paper gives new proofs of two well known results about a linear space been decomposable into the direct sums of invariant cyclic subspaces,using only linear algebra,while the known proofs of those results have to depend on the theory of finitely generated module on a principal ideal domain.

关 键 词：线性空间 直和分解 线性变换 循环不变子空间 

分 类 号：O177.3[理学—数学]