TITLE:
A Further Result on the Cyclic Subspace
AUTHORS:
Huailei Wang
KEYWORDS:
Power Kernel, Power Image, Cyclic Subspace, Jordan Block Matrix, Linear Map
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.4 No.2,
May
15,
2014
ABSTRACT: Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map on its cyclic subspace. By this result, a new approach of proof is found for the fact that a square matrix with only one eigenvalue and one-dimensional eigenspace is similar to a Jordan block matrix.