Self-similar matrices? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T14:58:38Z http://mathoverflow.net/feeds/question/10700 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/10700/self-similar-matrices Self-similar matrices? Igor Korepanov 2010-01-04T12:12:19Z 2010-01-05T22:28:53Z <p>Does anyone know anything about self-similar (infinite) matrices, with more or less fractal(-like) structure and admitting meaningful matrix-algebra operations?</p> http://mathoverflow.net/questions/10700/self-similar-matrices/10854#10854 Answer by Scott Morrison for Self-similar matrices? Scott Morrison 2010-01-05T22:20:09Z 2010-01-05T22:28:53Z <p>You should learn about the hyperfinite <code>II_1</code> factor, which is the limit of the inclusions</p> <pre><code>M_1 --&gt; M_2 --&gt; M_4 --&gt; M_8 --&gt; .... </code></pre> <p>(here <code>M_k</code> is the <code>k</code> by <code>k</code> matrices over \$\mathbb{C}\$) where each inclusion is given by tensoring with the identity matrix in <code>M_2</code>. Every 'finite' element is "self-similar" in a sense.</p>