Definition from Wiktionary, the free dictionary
Jump to navigation Jump to search


I've read the definition. I still don't understand what this is. Widsith 07:47, 14 April 2007 (UTC)

The definition is concise, even if it's difficult to understand. An understandable definition would require a chapter in a textbook (and usually does). --EncycloPetey 17:43, 11 April 2007 (UTC)

Hmm, well looking at the Wikipedia page it seems to me that one definition could be "a factor of multiplication representing the extent to which a vector is deformed in a given transformation". I'm no expert though. I'm looking at the OED now, which defines it as "One of those special values of a parameter in an equation for which the equation has a solution", which also seems a bit less opaque than what we have. I have a maths A-level so if I can't understand it I don't have much hope for a casual user (if any casual user would look this kind of thing up..!) Widsith 14:13, 12 April 2007 (UTC)
The Wikipedia page is using a particualr application of eigenvalues to define it. It would be like defining apple as "a product of vegetation representing the seed-carrying vessel in a reproductive event." It's an understandable definition, but it tells you more about the perceived purpose of the apple than what it is. It's too specific because eigenvalues turn up in situations other than vector products. The OED definition is appallingly vague, but I suppose something like it could be used as a supplementary gloss to our current definition. --EncycloPetey 16:25, 12 April 2007 (UTC)
OK, but our definition seems to be using a particular application of eigenvalues as well, that of linear algebra. Further down the 'Pedia page we have "The eigenvalue of a non-zero eigenvector is the scale factor by which it has been multiplied" which also seems a good working def. Your apple comparison is not very convincing I'm afraid! You obviously understand this better than me, but surely you can see that we need some definition that allows non-mathematicians to grasp the concept? Widsith 08:04, 13 April 2007 (UTC)
No, because that definition requires that you have a non-zero eigenvector. The concept spans several areas of mathematics because a vector is actually a form of matrix. A vector is simply a matrix with just one row (or column), so the matrix definition is actually broader than the vector-based definition. Any definition based on vector deformation will therefore be more restrictive because it eliminates the broader picture. The difficulty lies in creating a concise definition that is (1) accurate, and (2) accessible. The concept of eigenvalue is one that even I as a mathematician have had trouble with. It took me more than a week to comprehend what was going on when I first learned this word, and I had already had two courses in matrix algebra and differential calculus at the time. I hate to say it, but I haven't yet come across a good way to define the term eigenvalue so that it could be easily understood. We have have to just stick with a complicated efinition for now and refer readers to the WP article for deeper understanding. --EncycloPetey 22:07, 13 April 2007 (UTC)
If you say so. I'll copy this discussion to the talk page. Widsith 07:44, 14 April 2007 (UTC)

Some nice work has been done here. However, I don’t think the usage note is of much use: it is technical and doesn’t belong in a dictionary. H. (talk) 23:33, 27 April 2007 (UTC)