Generate random irreducible matrix

[Tenens]

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 $H_i$ with purely random numbers
• Creating the matrix by assigning element $A_{ij} = \min(1,\exp[\beta (H_i-H_j)])$

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?

 

[fresh_42]

Simply generate a random matrix with real values. The regular as well as irreducible ones are dense in the vector space of all matrices, so a random choice is almost always of the desired form.