This article is rated Stub-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Mathematics Low‑priority This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles Low This article has been rated as Low-priority on the project's priority scale.

Wikipedia already has an article on the Rayleigh quotient of a matrix:

   (
http://en.wikipedia.org/wiki/Rayleigh_quotient)

Please consider adding a hyperlink to that article here.

Done! silly rabbit ( talk) 18:54, 1 May 2008 (UTC) reply

The article on the field of values predates this article by a year. I recommend merging the content of Numerical Range into field of values. LachlanA ( talk) 23:36, 14 July 2009 (UTC) reply

I suggest the other way around: merging field of values into this article. I think "numerical range" is more commonly used. -- Taku ( talk) 23:48, 14 July 2009 (UTC) reply

I agree with merging field of values into this article instead. I personally hear the term "numerical range" more frequently as well, and also the recent work on higher-rank numerical ranges and joint numerical ranges never seems to use the term "field of values", so it seems to me that that term is going by the wayside in the current literature. JokeySmurf ( talk) 00:30, 15 July 2009 (UTC) reply

I agree to merge field of values into this article. Current research is presented at a bi-annual meeting called the Workshop on Numerical Range and Radii. Pzisme ( talk) 18:02, 10 October 2009 (UTC) reply

Agree wshun ( talk) 07:48, 16 August 2010 (UTC) reply

Seconded -- Mathuvw ( talk) 10:53, 29 March 2011 (UTC) reply

• Comment. The consensus above seems to be to merge, but no one is following through to do the merging. The discussion is stale, with no comments for over a year. In the absence of anyone performing the merge, I will remove the merge proposal template, without prejudice to anyone actually doing the work to merge. TJRC ( talk) 23:57, 27 November 2012 (UTC) reply

This article could be improved by writing down why numerical range is important, rather than just giving the definition. Specifically there's a result stated in Trefethen and Embree's book "Spectra and Pseudospectra" to the effect that the maximum real value of the numerical range of A gives a growth estimate for ||exp(At)|| near zero. Ewjw ( talk) 07:02, 26 February 2010 (UTC) reply

Is ist possible to define anywhere, what the vector X contains in the defining formula? And if X is a vector, how can then the scalar W(A) be a field? --Gotti 21:57, 17 October 2013 (UTC) — Preceding unsigned comment added by Druseltal2005 ( talk • contribs)