Prove that permutation matrices can be written as the product of transpositions.

So geometrically, we can represent transpositions as lines between two "poles" or sticks. And completing the cycle defines a permutation?

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- May 24th 2009, 11:17 AMmanjohn12permutation matrix
Prove that permutation matrices can be written as the product of transpositions.

So geometrically, we can represent transpositions as lines between two "poles" or sticks. And completing the cycle defines a permutation? - May 24th 2009, 02:15 PMNonCommAlg
for any $\displaystyle \alpha, \beta \in S_n,$ let $\displaystyle P_{\alpha}, P_{\beta}$ be the corresponding permutation matrices. then $\displaystyle P_{\alpha}P_{\beta}=P_{\beta \alpha }.$ now use this fact that every $\displaystyle \sigma \in S_n$ is a product of transpositions.

- May 24th 2009, 02:44 PMmanjohn12
because every transposition matrix is a permutation?

- May 24th 2009, 02:50 PMNonCommAlg
- May 24th 2009, 10:27 PMSwlabr
- May 25th 2009, 01:12 PMmanjohn12
- May 25th 2009, 11:30 PMNonCommAlg