Wikipedia:Featured article candidates/Eigenvalue, eigenvector and eigenspace/archive1

Eigenvalue, eigenvector and eigenspace
Partial Self-nom. This article was a mathematics collaboration of the week and is the result of many mergings. This is a very central topic in mathematics and applied disciplines which is taught during the early university classes in mathematics. It is referred more than 450 times on Wikipedia. A big well-balanced effort has been put on pedagogics, properties and theorems, and applications. The article covers also eigenfunction and eigenstate which are now redirected here. Vb 13:10, 11 October 2005 (UTC)
 * support and nominate Vb 13:15, 11 October 2005 (UTC)
 * support although a bit too much math for my liking. Non-mathematicians might have some trouble with this. Borisblue 18:04, 11 October 2005 (UTC)
 * Support. Because it is in clearly differentiated sections, it is useful for the layman and the mathematician alike. An excellent article. Si sic solum omnium.... Batmanand 19:57, 11 October 2005 (UTC)
 * Support. This article is awesome! -- Rune Welsh | &tau;&alpha;&lambda;&kappa; | Esperanza  21:21, 11 October 2005 (UTC)
 * Object
 * The image Image:Discrete-continuum.gif is claimed as "fair use". There's no reason to use fair use images in this article.
 * I have changed the description of the image. Could you please check whether it is OK now. Vb 09:24, 12 October 2005 (UTC)
 * It's a published, copyrighted work. That means that we either need to get the image released under a license such as the GFDL, or that it be used as "fair use", and I don't think a fair use claim can be justified here. --Carnildo 20:59, 12 October 2005 (UTC)
 * No it is not copyrighted. Don't mix up book of abstracts with proceedings.  I sent a mail to the author so that he can put an end to this discussion.  Vb 09:54, 13 October 2005 (UTC)
 * Was the image published in the US after 1989? If so, then unless the author has explicitly disclaimed copyright on it, it's copyrighted.  It's very hard to create a non-copyrighted work these days. --Carnildo 17:50, 13 October 2005 (UTC)
 * The author responded and allowed me explicitly to use the figure. I think this closes the case, doesn't it? Vb 10:01, 14 October 2005 (UTC)
 * Not neccessarily.  Was it "permission to use the figure on Wikipedia", or "permission to use under the GFDL"?  The second is acceptable, the first isn't. --Carnildo 19:57, 14 October 2005 (UTC)
 * The image Image:HAtomOrbitals.png is claimed as GFDL, but does not indicate the source or creator. The GFDL license requires this.  It's probably GFDL-self, but you should contact the uploader to verify this.
 * I contacted the author. This image is already on the featured article quantum mechanics. Vb 09:24, 12 October 2005 (UTC)
 * The image Image:Eigenfaces.png has no source or copyright information. This is grounds for speedy-deletion of the image.
 * I changed the description of the image. Since ORL is a public domain database, I think it is no problem.  Thank you for checking. Vb 09:24, 12 October 2005 (UTC)
 * The database may be public domain, but as I understand it, It's a database of faces. Depending on the origin of the eigenfaces in this image, it may or may not be in the public domain. --Carnildo 20:59, 12 October 2005 (UTC)
 * The database is not accessible anymore from the original site which distributed it. It was made of ten photographs of 40 persons.  The eigenfaces are a mixing of all those photographs. If the database is public domain, it means the photographs are in the public domain.  Well at least in my understanding: I am no lawyer. Vb 09:54, 13 October 2005 (UTC)
 * Is there some standard eigenface algorithm, or is there some element of creativity involved in the creation of the eigenface images? --Carnildo 17:50, 13 October 2005 (UTC)
 * I don't really know. Couldn't we assume good faith in this case? --Vb 10:01, 14 October 2005 (UTC)
 * --Carnildo 04:22, 12 October 2005 (UTC)


 *  Object  1) images are too large, esp. for smaller resolutions. Scale to between 220 to 270px. done 2) ToC is granulated, and contains too many subheadings. Specifically 5.1.x and 5.2.x should go. Rename 6 to something shorter. done =Nichalp   «Talk»=  15:27, 12 October 2005 (UTC)
 * Point 1) has been addressed. Point 2) is not valid:  This specific choice of titles and subtitles must be criticized on nonformal ground.  This article is intended to a very large audience ranging from the layman to the mathematician.  This particular choice of headings correspond to this. Applying blindly the FA criteria leads to an artificial uniformisation of WP which is not desired by many WPedians. Vb 08:19, 13 October 2005 (UTC) I did all you asked for blindly just to close the discussion. Vb 09:01, 13 October 2005 (UTC)
 * Please do not strike out a reviewer's objection. I evaluate all articles before objecting, and I never blindly apply the same formula to all articles. A single paragraph does not make a section and this criteria certainally applies to a mathematics article. Use the semicolon to create a non-sectional heading instead. See the ; in operation in the cricket article. =Nichalp   «Talk»=  05:22, 14 October 2005 (UTC)
 * Yes. That's what I did: I have used the ";".  I stroke out the part of your objections which are utterly objective and have been definitively addressed. Vb 09:12, 14 October 2005 (UTC)
 * I have some more issues:
 * (from a vector space to itself) : "(" ")" deviates from the text, please avoid such a use in the lead.
 * This remark is important because we have to specify which type of transformations we are speaking about. I have put it as a footnote.  Do you think it is better? Vb 17:36, 14 October 2005 (UTC)
 * see Fig. 1, for an informal definition). --> not needed in lead
 * Please discuss this issue with Kappa, I have included this to answer one of his remarks. See below. Vb 17:36, 14 October 2005 (UTC)
 * Parentheses other, possibly nonlinear, transformations could also be listed)—may be visualized by the effect they produce on vectors (arrows pointing from one point to another). deviation: Please flow the text. (This applies to all such elements henceforth)
 * Sorry but we have to define what we are speaking about (as when we speak about Green's operators) :-) Vb 17:36, 14 October 2005 (UTC)
 * See also: eigenplane --> unbold and use see also
 * doneVb 17:36, 14 October 2005 (UTC)
 * Earth rotates, earth is a common noun. use small caps.
 * No see article Earth. We are speaking about the planet.Vb 17:36, 14 October 2005 (UTC)
 * As another example, consider a thin the tone needs to be encyclopedic rather than text book style. "Consider" has to be removed.
 * Yes that's true that's a sickness of many math articles. I have tried to improve this.Vb 17:36, 14 October 2005 (UTC)
 * (see Spectral theorem) not necessary; already linked
 * I think we need it here to tell the reader where the particular conditions can be found
 * This provides an easy proof that the geometric multiplicity is always less than or equal to the algebraic multiplicity. (Do not confuse this 1st sense with generalized eigenvalue problem, below.) same problem, this has to have an encyclopedic tone, and should not read like a manual. This applies to all elements again.
 * I have tried to address this.Vb 17:36, 14 October 2005 (UTC)
 * Green's operator? Please explain
 * Done Vb 17:36, 14 October 2005 (UTC)
 * =Factor analysis=, =Tensor of inertia=; =Tensor of inertia= need to be expanded to twice its current length to be called a section. Please expand or else use the semicolon.
 * I think it is important that the reader can see in the TOC which are the possible application or at least which are listed in this article. I therefore don't change this. Vb 17:36, 14 October 2005 (UTC)
 * I think there should be some introduction to ease a reader into the subject. That it has to do with matrices, vectors and so on. I do have some knowledge on EV, so I feel that the introduction should ease users into the subject. =Nichalp   «Talk»=  16:40, 14 October 2005 (UTC)
 * I have added the links to linear algebra and functional analysis in the head. Do you think it helps the reader in the direction you point at? Vb 18:05, 14 October 2005 (UTC)
 * No, I'm not satisfied. I'll have a go at the article tomorrow. =Nichalp   «Talk»=  19:30, 14 October 2005 (UTC)
 * I've edited the text to withdraw my objection. =Nichalp   «Talk»=  15:18, 16 October 2005 (UTC)

It is a good idea to also have an informal introduction to the topic, without rigor, suitable for a high school student or a first-year undergraduate, as appropriate. For example,
 * Support. It's one of the best Mathematics articles I've seen. CO GDEN  19:53, 13 October 2005 (UTC)
 * Support - I'm a non-math guy and I thought it was neat. KingTT 21:56, 13 October 2005 (UTC)
 * Oppose, I can't tell what these things are without scrolling down. Definitions and examples should be front-loaded. Kappa 01:55, 14 October 2005 (UTC)
 * I do have to agree there. That's one ground for improvement, but it can be easily fixed. I still support. CO GDEN  02:24, 14 October 2005 (UTC)
 * This opposition makes sense. In order to address it, let me first cite the WP recommandations for a mathematics article
 * In the case of real numbers, a continuous function corresponds to a graph that you can draw without lifting your pen from the paper, that is, without any gaps or jumps.

The informal introduction should clearly state that it is informal, and that it is only stated to introduce the formal and correct approach. If a physical or geometric analogy or diagram will help, use one: many of the readers may be non-mathematical scientists. Thus I think it would be a bad idea simply to shift the definitions and examples from the body to the head. That's the reason why I made the Mona Lisa picture. I think the caption provides exactly what is required as a definition. To make this point clear I have numbered the figures and refer to Fig. 1 in the head. I think someone reading its caption will understand what is the topic even without much mathematics knowledge. Tell me whether you agree. Vb 09:12, 14 October 2005 (UTC)
 * Can you rewrite the description so the example will work for someone who can't see the image? Kappa 12:11, 14 October 2005 (UTC)
 * I have tried to rewrite the caption from this point of view. Is it better now? Vb 14:09, 14 October 2005 (UTC)
 * Thanks, that helped. I also added something so that a user who can't see the image will hopefully be able to imagine what happened. I have withdrawn my opposition. Kappa 15:02, 14 October 2005 (UTC)
 * What you added has a good intention but is not correct. This transformation is named shear.  The problem is that tranfo is not easily defined for non mathematicians.  It is easly defined graphically in an example but not with words.  I therefore think it is better to let it as it was before. Vb 15:44, 14 October 2005 (UTC)
 * I think I have found a formulation which cope with this problem Vb 16:32, 14 October 2005 (UTC)
 * Support: The illustration using the Mona Lisa at the beginning is ingenious! Mamawrit  es    & listens  10:06, 14 October 2005 (UTC)