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Let T be a linear operator such that T=D+N is a jordan decomposition of T. That...

Let T be a linear operator such that T=D+N is a jordan decomposition of T. That is, D is diagonalizable and N is Nilpotent. Show if S is an endomorphism of V, that is, if S is a linear operator with domain and codmain V, prove if T commutes with S, (ST=TS), then D commutes with S (DS=SD), and N commutes with S (NS=SN).
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