I have here the definition:
Let T be a linear operator on a finite-dimensional vector
space V over the field F. The minimal polynomial for T is the (unique)
monic generator of the ideal of polynomials over F which annihilate T.
I would like to know how to prove the uniqueness of it, how would I start?
Answer
You can start with proving
If f(T)=g(T)=0 for some polynomials f,g, then gcd
and then the uniqueness will follow from a simple proof by contradiction.
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