Assertion: permutation matrix | /r/HasProperty | p π
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Source sentences:
text: For example, the permutation matrix P π corresponding to the permutation : π = ( 1 2 3 4 5 1 4 2 5 3 ) , {\displaystyle \pi ={\begin{pmatrix}1&2&3&4&5\\1&4&2&5&3\end{pmatrix}},} is
text: To calculate the eigenvalues of a permutation matrix P σ {\displaystyle P_{\sigma }} , write σ {\displaystyle \sigma } as a product of cycles, say, σ
text: Again, repeated application of this result shows that post-multiplying a matrix M by the permutation matrix P π , that is, M P π , results in permuting the columns of M. Notice also that
text: Given two permutations π and σ of m elements, the corresponding permutation matrices P π and P σ acting on column vectors are composed with