User quantumleak - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T03:58:45Z http://mathoverflow.net/feeds/user/16292 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88440/bounding-largest-eigenvalue Bounding largest eigenvalue QuantumLeak 2012-02-14T16:31:37Z 2012-02-15T00:48:10Z <p>Hi all, </p> <p>do you know how to compute (as a function of n) the largest eigenvalue of this matrix (or at least to bound it)?</p> <p>$$\left(\begin{array}{cccccc} 0 &amp; 1 &amp; &amp; &amp; &amp; \cr 1 &amp; 0 &amp; \sqrt 2 &amp; &amp; &amp; \cr &amp; \sqrt 2 &amp; 0 &amp; &amp; &amp; \cr &amp; &amp; &amp; \ddots &amp; &amp; &amp; \cr &amp; &amp; &amp; &amp; 0 &amp; \sqrt n &amp; \cr &amp; &amp; &amp; &amp; \sqrt n &amp; 0 &amp; \end{array}\right)$$</p> <p>Thanks!</p> http://mathoverflow.net/questions/88440/bounding-largest-eigenvalue Comment by QuantumLeak QuantumLeak 2012-02-15T10:40:20Z 2012-02-15T10:40:20Z @Noam: where can I find a reference for the bounding of $L_m$? http://mathoverflow.net/questions/88440/bounding-largest-eigenvalue Comment by QuantumLeak QuantumLeak 2012-02-15T10:07:46Z 2012-02-15T10:07:46Z This come from physics, it is the representation of the sum of annihilation and creation operators on a bounded boson Fock space.