How to taker power of a permutaion matrix

Hi ,I want to find the power of a permutation matrix, i.e

A=(1 2 3;3 2 1) is a permutation matrix and I want to find (1 2 3; 3 2 1)^5

.How to do this in matlab

Answer 1

[Bruno Luong]

You have 2 ways to compute it, from the permutation itself, or using the permutation matrix then raise a power of it.

% Generate a random test permutation
[~,p]=sort(rand(1,10)); % in you case it's [3 2 1], the second row of your A

% Permutation matrix 
p0 = 1:length(p);
A = accumarray([p(:) p0(:)],1);

% raise power
n = 5;
Apn = A^n

% apply the permutation n times 
pn = p0;
for k=1:n
    pn = pn(p);
end
An = accumarray([pn(:) p0(:)],1)

% Check both gives the same result 
isequal(Apn,An)