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A Further Result on the Cyclic Subspace
State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China
- 1 State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China
Advances in Linear Algebra & Matrix Theory·Volume 04 (2014)·Pages 96–99·Published 15 May 2014·DOI10.4236/alamt.2014.42007
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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.
KeywordsPower KernelPower ImageCyclic SubspaceJordan Block MatrixLinear Map
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