User quantumleak - MathOverflowmost recent 30 from http://mathoverflow.net2013-05-26T03:58:45Zhttp://mathoverflow.net/feeds/user/16292http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/88440/bounding-largest-eigenvalueBounding largest eigenvalueQuantumLeak2012-02-14T16:31:37Z2012-02-15T00:48:10Z
<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>$$
\left(\begin{array}{cccccc}
0 & 1 & & & & \cr
1 & 0 & \sqrt 2 & & & \cr
& \sqrt 2 & 0 & & & \cr
& & & \ddots & & & \cr
& & & & 0 & \sqrt n & \cr
& & & & \sqrt n & 0 &
\end{array}\right)
$$</p>
<p>Thanks!</p>
http://mathoverflow.net/questions/88440/bounding-largest-eigenvalueComment by QuantumLeakQuantumLeak2012-02-15T10:40:20Z2012-02-15T10:40:20Z@Noam: where can I find a reference for the bounding of $L_m$?http://mathoverflow.net/questions/88440/bounding-largest-eigenvalueComment by QuantumLeakQuantumLeak2012-02-15T10:07:46Z2012-02-15T10:07:46ZThis come from physics, it is the representation of the sum of annihilation and creation operators on a bounded boson Fock space.