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If T is a nilpotent transformation from V -> V, V - finite dimensional vector space.

show that [tex]a_{0}+a_{1}T+\cdots+a_{k}T^{k}[/tex] is invertible. [tex]a_{0}[/tex] nonzero.

Im having trouble finding the inverse, I know for 1+T+[tex]\cdots[/tex]+T[tex]^{m-1}[/tex]

the inverse is (1-T),where T[tex]^{m}[/tex]=0. I also tried [tex]a_{0}^{-1}T^{m-1}[/tex]

but this gives me [tex]T^{m-1}[/tex]

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# Homework Help: Nilpotent Operator

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