Linear transformation $T\colon V \to V$ has the property that there is no non-trivial subspace $W$ for which $T(W) \subseteq W$ . Prove that for every polynomial $P$ , $P(T)$ is either invertible or zero.
No non-trivial subspace is invariant under $T$, then $P(T)$ is inveritble
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linear-algebra
matrices
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0Thanks for point my mistake, I edit it just now ;) – 2012-02-16
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2And, you may consider accepting answers to your previous queries by clicking on the tick mark beside your favorite answer. Note that this is the only way to thank people who care for you on this site :) – 2012-02-16
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0The entire space is itself a non-trivial subspace $W$ for which $T(W) \subseteq W$. I'm certain that non-trivial *proper* subspaces are what was intended. – 2012-02-16