eigenvector en · NOUN
Pronunciation
- (US) audio
Etymology
From eigen- + vector, a partial calque of German Eigenvektor. The prefix eigen- (also used in eigenvalue) was first used in 1904, by David Hilbert, and was possibly inspired by a related usage by Hermann von Helmholtz.
Meanings
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A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
Both equations give the relation x₁ = −x₂. Therefore the set of eigenvectors corresponding to λ = 2 is given by: […] An eigenvector corresponding to λ₁ = 2 is ( −1 1 ).
2025 March 22 (last accessed), “Lesson 11”, in University College London, archived from the original on 06 Oct 2021, 8.2 Method to find eigenvalues and eigenvectors, page 1:
- A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| eigenvectors | Number=Plur | lexicographic |
Deriveds
eigenbivector · left eigenvector · right eigenvector · eigenvectorial
Relateds
eigendecomposition · eigensystem · eigenbrain · eigentheory · eigenmode · eigenvalue · eigenstate · eigenhead · eigenspace · eigenspinor · eigenpair · Mathworld article on eigenvectors · eigenfunction · eigenface · eigenbasis
Synonyms
proper vector · characteristic vector · latent vector
Translations (34)
es eigenvector (vector not rotated by linear transformation) · es vector propio (vector not rotated by linear transformation) · is eiginvigur (vector not rotated by linear transformation) · et omavektor (vector not rotated by linear transformation) · cmn 本徵向量 /本征向量 (vector not rotated by linear transformation) · hu sajátvektor (vector not rotated by linear transformation) · ca vector propi (vector not rotated by linear transformation) · fi ominaisvektori (vector not rotated by linear transformation) · cy fector eigen (vector not rotated by linear transformation) · no eigenvektor (vector not rotated by linear transformation) · gl autovector (vector not rotated by linear transformation) · nb egenvektor (vector not rotated by linear transformation) · hi अभिलक्षणिक सदिश (vector not rotated by linear transformation) · fr vecteur propre (vector not rotated by linear transformation) · is eiginvektor (vector not rotated by linear transformation) · ja 固有ベクトル (vector not rotated by linear transformation) · gl eigenvector (vector not rotated by linear transformation) · sv egenvektor (vector not rotated by linear transformation) · nl eigenvector (vector not rotated by linear transformation) · el ιδιοδιάνυσμα (vector not rotated by linear transformation) · pl wektor własny (vector not rotated by linear transformation) · pt vetor próprio (vector not rotated by linear transformation) · pt autovetor (vector not rotated by linear transformation) · de Eigenvektor (vector not rotated by linear transformation) · es autovector (vector not rotated by linear transformation) · ast vector propiu (vector not rotated by linear transformation) · gl vector propio (vector not rotated by linear transformation) · it autovettore (vector not rotated by linear transformation) · cmn 特徵向量 /特征向量 (vector not rotated by linear transformation) · ast autovector (vector not rotated by linear transformation) · he וֶקְטוֹר עַצְמִי (vector not rotated by linear transformation) · ru со́бственный ве́ктор (vector not rotated by linear transformation) · ro vector propriu (vector not rotated by linear transformation) · da egenvektor (vector not rotated by linear transformation)