Let $V$ be a vector space of dimension $n$. For each positive integer $k$, does there is a linear transformation $T: V \rightarrow V$, such that $ker(T^k) = Im(T^k)$ ?.
For $k=1$, such a linear map exist. What about for $k >1$ ?
For each $k$, does ther exist a linear transformation $T: V \rightarrow V$ such that $ker(T^k) = Im(T^k)$
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linear-transformations
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0What if n=dim V is odd? – 2017-01-20
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0@MathChat for $k=1$, $dim(V)$ is even. – 2017-01-20