## 每週問題 May 27, 2013

Let $P$ be an $n\times n$ idempotent matrix, i.e., $P^2=P$. Prove that $\mathrm{rank}P=\mathrm{trace}P$.

$\mathbf{0}=P\mathbf{x}=P^2\mathbf{y}=P\mathbf{y}=\mathbf{x}$

PowSol-May-27-13

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