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

Synopsis

A permutation $p$ acts on the space of $n \times n$ matrices by permuting the rows of the matrix according to the permutation.

The permutation cannot permute more than numRows 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 : p * A

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

              3       3
o3 : Matrix ZZ  <-- ZZ

The permutation can be a permutation on less than numRows 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 |

              3       2
o5 : Matrix ZZ  <-- ZZ

i6 : p * A

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

              3       2
o6 : Matrix ZZ  <-- ZZ

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