Talk:Eigenvector
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It was wrong to redirect eigenvalue to eigenvector. Vectors aren't the only things that can have the, as it were, "eigen-" idea applied to them. For instance, eigenfunctions have eigenvalues. PML.
- I agree that it is wrong to redirect eigenvalue to eigenvector and I have corrected this. But your reason is incorrect. Eigenfunctions are vectors in the linear space of functions. wshun
- Note that for infinite dimensional Hilbert spaces, eigenstates only exist in an extension of that space. For example, Dirac delta functions only exist in an extension of L2(R).
Is this really true for all eigenvectors of all linear operators? What about, for example, the stationary states of the hydrogen atom, which are eigenvectors of the Hamiltonian? Josh Cherry 21:35, 14 Oct 2003 (UTC)
Eigen has some different meanings in German, and there's also a nobel prize winner with that name. In the FAQ of the German newsgroup de.etc.sprache.deutsch [1] (http://faql.de/etymologie.html#eigen) they state that the names for "eigenvalue" and "eigenvector" come from the meaning "inherent, characteristic". nikai
- Can anyone confirm that the German (or Dutch) word "eigen" is indeed the correct etymology of the words eigenvalue and eigenvector (besides the German etymology faq from above)? It would suggest that a German or Dutch mathematician was the first to use these terms, but I can't find any references of this. Who was first to name an eigenvector an eigenvector? --Anthony Liekens 15:04, 1 Jan 2005 (UTC)
- According to [2] (http://members.aol.com/jeff570/e.html), David Hilbert first used Eigenwert in 1904. Hermann von Helmholtz coined similar words earlier (like Eigentöne, which were translated as proper tones). -Nikai 14:42, 17 Mar 2005 (UTC)
How about adding some examples what eigenvectors can be used for? Some simple examples for a non-mathematician to understand why we need to know about them. Are they useful for programming, for example? 3D graphics?