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Permutation Matrix Diagonalization
I came across this question while solving this problem in my textbook. Does anyone know how to solve this question?
A:
You can start by writing out $\begin{pmatrix} 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0\end{pmatrix}$, which tells you the effect of these transformations on a vector.
So, first of all, we need to make the matrix upper triangular, by deleting one of the diagonals, since that will correspond to a transposition followed by a reflection:
$$\begin{pmatrix} 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix} \rightarrow \begin{pmatrix} 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix} = \begin{pmatrix} 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}\begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}.$$
One transposition corresponds to
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Yeah, I know it’s the new XP version. I got the game on my DVD yesterday and was planning to install and play tonight. Unfortunately, I have the FOL installed on my desk top and have lost the disk. I’ll have to do an installation from a cd. But I want to know if there is a list of compatible games that work on the FOL.
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