How to taker power of a permutaion matrix

Question

sadiqa ilyas 2019-10-5

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https://ww2.mathworks.cn/matlabcentral/answers/483708-how-to-taker-power-of-a-permutaion-matrix

编辑： Bruno Luong 2019-10-5

采纳的回答： Bruno Luong

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

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Answer 1

Bruno Luong 2019-10-5

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https://ww2.mathworks.cn/matlabcentral/answers/483708-how-to-taker-power-of-a-permutaion-matrix#answer_394925

编辑：Bruno Luong 2019-10-5

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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)