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.
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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.
