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Given an endomorphism A over a finite dimensional vector space havingJordan-Chevalley decomposition, the lattices of invariant and hyperinvariantsubspaces of A can be obtained from the nilpotent part of this decomposition.We extend this result for lattices of characteristic subspaces. We also obtaina generalization of Shoda's Theorem about the characterization of the existenceof characteristic non hyperinvariant subspaces.

The lattice of characteristic subspaces of an endomorphism with Jordan-Chevalley decomposition