实线性空间上线性变换的循环子空间  

Cyclic Subspace of Linear Transformation on Real Linear Space

作　　者：张新发[1] ZHANG Xin-fa(Department of Mathematics, East China University of Science & Technology, Shanghai 200237, China)

机构地区：[1]华东理工大学数学系

出　　处：《大学数学》2019年第3期77-81,共5页College Mathematics

摘　　要：对于实数域上线性空间的线性变换的根子空间,给出了类似于复数域情形的循环子空间的分解,分为实循环子空间和复循环子空间两种.证明了无论哪种循环子空间,都有类似于复数域情形的一个重要结果:循环子空间不可以分解为两个非零不变子空间的直和.We give the decomposition of a root subspaces into cyclic subspaces of a linear transformation on a real linear space, which is similar to that of complex field. Moreover, we prove that for both the real and complex cases, a cyclic subspace can not be decomposed into direct sum of two nonzero invariant subspaces. The results are valuable to the learning of linear transformation and give a comprehensive understanding to related topics.

关 键 词：根子空间 实循环子空间 复循环子空间 

分 类 号：O151.21[理学—数学]