Find the minimal polynomial of T: R^3→R^3 defined by T(a,b,c)= (a-b,b,c)
We seek eigenvalues of this operator:
.
This implies that and .
The only value of which provides a non-zero solution is .
Therefore, the characteristic polynomial of T is (x-1)3.
The minimal polynomial is a factor of the characteristic polynomial (x-1)3.
It may be (x-1)3, (x-1)2 or x-1. Check them all.
, T-E is not a zero operator.
, hence, (T-E)2=0.
Therefore, the minimal polynomial of T is (x-1)2.
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