Talk:eigen-

Usage

I'm putting this on the talk page because it's slightly tricky, and there should be a place to disagree with me.

In general, eigen- refers to eigenvectors: an eigenstate is an eigenvector in a vector space consisting of states; an eigenfunction is an eigenvector in a vector space consisting of functions, and so on. Eigenvalue is an exception to this, not an example of it: while an eigenvector's eigenvalue is a number, and thus part of a vector space, the linear operator defined on the eigenvector and its vector space is not, normally, defined on numbers.

I don't think it's ever helpful to translate eigen- as own. My suggestion would be to define it as eigenvector. An eigenfunction is an eigenvector function, and so on.

46.115.74.77 16:09, 27 November 2012 (UTC)

Okay, it turns out there are more exceptions than I thought: eigenpair and eigenspace aren't vectors; an eigensolver is an algorithm; and a "Hecke eigensheaf" is a mathematical construction I don't understand at all. Here's the list of eigen-prefixed redlinks:

• probably eigenvectors:
  • eigenchannel
  • eigencolor
  • eigencontent
  • eigendirection
  • eigenpotential
  • eigenvariable
  • eigenwave
• probably other things:
  • eigenpair
  • eigenprojection
  • eigensheaf

I'll try finding the time to actually check what each means in the arXiv preprints.

46.115.99.214 17:27, 28 November 2012 (UTC)

Some more: eigenbrane, eigengroup, eigenvariety, eigenarray, eigenscale, eigenbundle, eigenlevel, eigenmap, eigenray, eigensample, eigenoscillation, eigendata, eigenangle. Equinox ◑ 07:00, 18 September 2015 (UTC)

I'd say that eigenvector and eigenvalue came first, partially calqued from Eigenvektor and Eigenwert. Then eigen- was abstracted as a prefixes meaning "to do with eigenvectors and eigenvalues". Oh, and you guys forgot eigenbasis and eigendecomposition. --AndreRD (talk) 11:17, 12 March 2015 (UTC)