Macaulay2 » Documentation
Packages » Permutations :: Matrix * Permutation
next | previous | forward | backward | up | index | toc

Matrix * Permutation -- computes the action of a permutation on the columns of a matrix

Synopsis

Description

A permutation $p \in \mathfrak{S}_n$ acts on the space of $m \times n$ matrices by permuting the columns of the matrix according to the permutation.

The permutation cannot permute more than numColumns M elements.

i1 : p = permutation {3,1,2}

o1 = Permutation{3, 1, 2}

o1 : Permutation
i2 : A = matrix {{1,2,3},{4,5,6},{7,8,9}}

o2 = | 1 2 3 |
     | 4 5 6 |
     | 7 8 9 |

              3       3
o2 : Matrix ZZ  <-- ZZ
i3 : A * p

o3 = | 2 3 1 |
     | 5 6 4 |
     | 8 9 7 |

              3       3
o3 : Matrix ZZ  <-- ZZ

The permutation can be a permutation on less than numColumns M elements.

i4 : p = permutation {2,1}

o4 = Permutation{2, 1}

o4 : Permutation
i5 : A = matrix {{1,2,3},{4,5,6}}

o5 = | 1 2 3 |
     | 4 5 6 |

              2       3
o5 : Matrix ZZ  <-- ZZ
i6 : A * p

o6 = | 2 1 3 |
     | 5 4 6 |

              2       3
o6 : Matrix ZZ  <-- ZZ

See also

Ways to use this method: