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Does this matrix come up anywhere?

  1. Sep 8, 2010 #1
    d-by-d matrix where d is a power of 2

    d,1,1,1,...
    1,d,1,1,...
    1,1,d,1,..
    ....

    In particular, I'm looking for nice expression for an orthogonal basis of eigenvectors of it
     
  2. jcsd
  3. Sep 9, 2010 #2

    Office_Shredder

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    You can decompose it into (d-1)I-A where A is the matrix with all 1's. The eigenvectors of A and (d-1)I-A are the same, so all you need to do is find the eigenvectors of the matrix with all ones.

    Since A has a big kernel and you get to pick whichever eigenvectors you want this should be doable
     
  4. Sep 9, 2010 #3
    +1 for office_shredder.

    and in answer to the question in your title - this type of matrix does come up in some physical systems... I just can't remember where I've seen it.

    Also, it's a very special type of http://en.wikipedia.org/wiki/Circulant_matrix
     
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