most recent 30 from http://mathoverflow.net 2013-05-18T12:33:29Z http://mathoverflow.net/feeds/question/110316 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110316/estimating-a-spectral-gap Felix Goldberg 2012-10-22T10:36:13Z 2012-10-22T10:36:13Z

<p>Suppose you have a real positive definite matrix $A$ who eigenvalues are $\lambda_{1} \leq \lambda_{2} \leq \ldots \leq \lambda_{n}$. I am interested in bounding from below $\lambda_{2}-\lambda_{1}$. (It is known that $\lambda_{1}$ is simple). Are there any known methods for this kind of problem?</p>