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I have a question for which I cannot find the answer around,

any help would be really appreciated.

Suppose we have a matrix A of a linear transformation of a vector space,

with only one eigenvalue, say 's'.

My question is: Is the operator (A-sI) nilpotent? ('I' is the identity matrix).

I am trying to understand the proof of the Jordan Canonical Form Theorem and there is

a fuzzy point in my notes about that...

Thanks a lot in advance..

EDIT: I am becoming pretty sure about that, but some confirmation would be great..

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# Nilpotency of Matrix with one eigenvalue

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