Diagonalizable linear transformations...
Suppose $V$ is a finite dimensional vector space over $\Bbb C$ and that
$T: V \rightarrow V$ is a linear transformation such that $T^4=I$. Prove
that $T$ is diagonalizable, and that this does not necessarily hold when
$V$ is taken over $\Bbb R$.
I haven't tried much on this since I do not know where to start really.
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