Meanings
plural eigenvectors
- linear algebraA 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 1Synonyms: characteristic vector, latent vector, proper vector
- engineeringA right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Synonyms & antonyms
nounA 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).
Origin
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.
Full word history & related roots →Translations
Catalan vector propi
- vector propivector not rotated by linear transformation
Chinese Mandarin 本徵向量 /本征向量, 特徵向量 /特征向量
- 本徵向量 /本征向量 (běnzhēng xiàngliàng)vector not rotated by linear transformation
- 特徵向量 /特征向量 (tèzhēng xiàngliàng)vector not rotated by linear transformation
Danish egenvektor
- egenvektorvector not rotated by linear transformation
Dutch eigenvector
- eigenvectorvector not rotated by linear transformation
Estonian omavektor
- omavektorvector not rotated by linear transformation
Finnish ominaisvektori
- ominaisvektorivector not rotated by linear transformation
French vecteur propre
- vecteur proprevector not rotated by linear transformation
German Eigenvektor
- Eigenvektorvector not rotated by linear transformation
Greek ιδιοδιάνυσμα
- ιδιοδιάνυσμα (idiodiánysma)vector not rotated by linear transformation
Hebrew וֶקְטוֹר עַצְמִי
- וֶקְטוֹר עַצְמִיvector not rotated by linear transformation
Hindi अभिलक्षणिक सदिश
- अभिलक्षणिक सदिश (abhilakṣaṇik sadiś)vector not rotated by linear transformation
Hungarian sajátvektor
- sajátvektorvector not rotated by linear transformation
Icelandic eiginvigur, eiginvektor
- eiginvigurvector not rotated by linear transformation
- eiginvektorvector not rotated by linear transformation
Italian autovettore
- autovettorevector not rotated by linear transformation
Japanese 固有ベクトル
- 固有ベクトル (koyū bekutoru)vector not rotated by linear transformation
Norwegian Bokmål egenvektor
- egenvektorvector not rotated by linear transformation
Norwegian Nynorsk eigenvektor
- eigenvektorvector not rotated by linear transformation
Polish wektor własny
- wektor własnyvector not rotated by linear transformation
Portuguese autovetor, vetor próprio
- autovetorvector not rotated by linear transformation
- vetor própriovector not rotated by linear transformation
Romanian vector propriu
- vector propriuvector not rotated by linear transformation
Russian со́бственный ве́ктор
- со́бственный ве́ктор (sóbstvennyj véktor)vector not rotated by linear transformation
Spanish vector propio, autovector
- vector propiovector not rotated by linear transformation
- autovectorvector not rotated by linear transformation
- eigenvectorvector not rotated by linear transformation
Swedish egenvektor
- egenvektorvector not rotated by linear transformation
Welsh fector eigen
- fector eigenvector not rotated by linear transformation
Cite this entry
eigenvector. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/eigenvector
“eigenvector.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/eigenvector. Accessed November 2, 2026.
WatkinsX Dictionary, s.v. “eigenvector,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/eigenvector.
Source: eigenvector on Wiktionary, CC BY-SA 4.0.