If a vector [tex]v\in V[/tex] and a linear mapping [tex]T:V\to V[/tex] are fixed, and there exists numbers [tex]\lambda_1\in\mathbb{C}[/tex], [tex]n_1\in\mathbb{N}[/tex] so that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

(T - \lambda_1)^{n_1}v = 0,

[/tex]

is it possible that there exists some [tex]\lambda_2\neq\lambda_1[/tex], and [tex]n_2\in\mathbb{N}[/tex] so that

[tex]

(T - \lambda_2)^{n_2}v = 0?

[/tex]

(Here complex numbers are interpreted as multiplication operators [tex]V\to V[/tex], [tex]v\mapsto \lambda v[/tex], as usual.)

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# Eigenvalue kind of nilpotent problem

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