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We have a linear transformation f:V-> V. The minimal polynomial is m(x)=(x-λ1)p1(x-λ2)p2. (i) Prove that V=V1+V2,(direct...

We have a linear transformation f:V-> V.

The minimal polynomial is m(x)=(x-λ1)p1(x-λ2)p2.

(i) Prove that V=V1+V2,(direct Sum) with V1=Ker(f-λ1Iv) and V2=Ker(f-λ2Iv) , λ1 non equal with λ2

(ii) Prove that V1 and V2 is invariant from f.

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