Exercise27.3

Write down the square matrix \(F\) such that

\begin{equation*} F \begin{pmatrix} x_1\\ x_2 \\ \vdots \\ x_m \end{pmatrix} = \begin{pmatrix} x_m\\ x_{n-1} \\ \vdots \\ x_1 \end{pmatrix}. \end{equation*}

Let \(E=(I+F)/2\text{.}\) Is \(E\) a projector? Is it an orthogonal projector?

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