sigma=mfb said:You can do it element by element. For example, 4 gets mapped to 6. What does 6 get mapped to? That will give you one entry in your matrix for sigma^2.
Alternatively, do it cycle by cycle with a similar approach.
No, 1->6 is a part of sigma2. This specific example happens to have some mappings common with its inverse because sigma3 keeps several elements unchanged, but that is pure coincidence.ilyas.h said:This is the wrong approach because by doing this, you're calculating (sigma)^-1, that's the inverse.
mfb said:No, 1->6 is a part of sigma2. This specific example happens to have some mappings common with its inverse because sigma3 keeps several elements unchanged, but that is pure coincidence.
Swap the two lines and sort the columns to make the first line "1 2 3 4 5 6" again.ilyas.h said:how would you find the inverse of the permutation then?
mfb said:Swap the two lines and sort the columns to make the first line "1 2 3 4 5 6" again.
This is equivalent to "for 1, look where it appears in the bottom line, find which elements gets mapped to 1, map 1 to this element" and so on.
A permutation matrix is a square matrix that represents a reordering of the rows or columns of the identity matrix. It is used in linear algebra to represent permutations of vectors or other matrices.
A permutation matrix is created by swapping the rows or columns of the identity matrix according to the desired permutation. Each row or column in the resulting matrix will contain exactly one 1 and the rest 0s.
The square of a permutation matrix represents the composition of two permutations. This means that if we multiply a permutation matrix by itself, the resulting matrix will represent the permutation that is obtained by performing the two permutations in succession.
The square of a permutation matrix can be calculated by simply multiplying the matrix by itself using standard matrix multiplication rules.
The square of a permutation matrix is always a permutation matrix itself. It is also invertible, meaning that it has an inverse matrix that represents the inverse permutation. Additionally, the square of a permutation matrix is always equal to the identity matrix.