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Generate random irreducible matrix

  1. Dec 26, 2011 #1
    Hi, I want to create a generator for random irreducible N times N matrices, where N is a given integer.

    For now I'm using this trick:
    • Generate a N-length array [itex]H_i[/itex] with purely random numbers
    • Creating the matrix by assigning element [itex]A_{ij} = \min(1,\exp[\beta (H_i-H_j)])[/itex]

    This matrix is guaranteed to be irreducible by a book I found. I was just wondering, does this method generate all kinds of irreducible matrices or just a subset?

    Is there any other algorithm to generate an irreducible matrix? Do you have any references on how to build such a random generator?
  2. jcsd
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