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Let E be the mxm matrix that extracts the "even part" of an m-vector; Ex=(x+Fx)/2 where...

Let E be the mxm matrix that extracts the "even part" of an m-vector; Ex=(x+Fx)/2 where F is the mxm matrix that flips {x1, ...,xm}* to {xm, ..., x1}*. What is (Ex)^2. I'm lost on how to calculate this.

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