eigenfunction

English

Etymology

From eigen- +‎ function.

Noun

eigenfunction (plural eigenfunctions)

1. (mathematics) A function $\phi$ such that, for a given linear operator $D$, $D\phi =\lambda \phi$ for some scalar $\lambda$ (called an eigenvalue).

Synonyms

• proper function, eigenstate

Related terms

• eigenbasis
• eigenbrain
• eigendecomposition, eigen decomposition
• eigenface
• eigenhead
• eigenmode
• eigenpair
• eigenspace
• eigenspinor
• eigenstate
• eigensystem
• eigentheory
• eigenvalue
• eigenvector

Translations

function

• Arabic: ^{(please verify)} دَالَة خَاصَّة f (dāla ḵāṣṣa)
• Chinese:

  Mandarin: 本徵函數／本征函数 (běnzhēng hánshù)

• Finnish: ominaisfunktio
• French: fonction propre (fr) f
• German: Eigenfunktion (de) f
• Greek: ιδιοσυνάρτηση f (idiosynártisi)
• Icelandic: eiginfall n
• Italian: autofunzione (it) f
• Japanese: 固有関数 (koyū kansū)
• Portuguese: autofunção f (Brazil), função própria f (Portugal)
• Russian: со́бственная фу́нкция f (sóbstvennaja fúnkcija)
• Spanish: autofunción f, función propia f
• Swedish: egenfunktion (sv) c

See also

• hamiltonian

Further reading

• Mathworld article on eigenfunctions