A Further Result on the Cyclic Subspace

Huailei Wang

State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China.

DOI: 10.4236/alamt.2014.42007                

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.

Keywords

Power Kernel, Power Image, Cyclic Subspace, Jordan Block Matrix, Linear Map

Conflicts of Interest

The authors declare no conflicts of interest.

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