most recent 30 from http://mathoverflow.net 2013-05-21T20:53:50Z http://mathoverflow.net/feeds/user/29757 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104009/condition-number-for-rayleigh-ritz-quotient/115736#115736 RLC 2012-12-07T19:10:42Z 2012-12-07T22:10:22Z

<p>If u is an eigenvector for an eigenvalue that is in the interior of the spectrum, then there is no such bound becomes there are numerous vectors that generate Rayleigh quotients for points in the convex hull of the spectrum. And as for Sharkos comment, you would want something like the sine of the angle between u and v.</p> <p>An absolute condition number for a Rayleigh quotient would look more like $|x^*Ax-y'Ay|&lt;=\kappa$(x'Ax) ||x-y||$, where K would be the condition number for x'Ax, where x and y are unit vectors. It shows how changes in the Rayleigh quotient can be bounded by changes in the vector.</p> <p>Your suggested condition number is more like the condition number for the generating vector. </p>