Given $P : R^n → R^n$ is a linear transformation. Show that there is an integer $k$ such that $R(P^k)=R(P^{k+1})=R(P^{k+2})=...$($R(P)$ denotes the range of $P$.)
Given $P : R^n → R^n$ is a linear transformation. Show that there is an integer $k$ such that $R(P^k)=R(P^{k+1})=R(P^{k+2})=...$
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linear-algebra