Finding the permutation matrix that "cyclic shifts"

Question

Find the permutation matrix $P_n$ that "cyclic shifts" $(1, 2, \dots, n)$ to $(2, 3, \dots , n,1)$.

Could you please help me solve this question?

If you know what kind of matrix can be a permutation matrix, you should be able to give the dimensions of the matrix right away. Then go through element by element and decide what each one must be. Can you be more specific about where you run into difficulty? — David K, Apr 13 '17 at 21:35

score 1 · Accepted Answer · answered Apr 13 '17 at 21:34

1

Hint:$$\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix} \begin{bmatrix} a \\ b \\ c\end{bmatrix} = \begin{bmatrix} b \\ c \\ a\end{bmatrix}$$

answered Apr 13 '17 at 21:34

Siong Thye Goh

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Finding the permutation matrix that "cyclic shifts"

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