Random permutation matrix

Question

Is there an easy way to simulate a random permutation matrix (say of size 1000 by 1000) in Matlab? I would like to study the eigenvalue distribution of independent sum of such matrices.

Thanks in advance!

Answer 1

You can generate a random permutation matrix like so:

1. Create a unity matrix:

   A = eye( N );  %// N is the size of your matrix
   

   For large values of N it is better to use sparse matrices:

   A = speye( N ); % create sparse identity matrix
   

2. Generate a random permutation:

   idx = randperm(1:N);
   

3. Use vector indexing to rearrange the rows accordingly

   A = A(idx, :);
   

Voila!