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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).
Definition source: English Wiktionary via Wiktextract
Topics: linear-algebra, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: characteristic vector, latent vector, proper vector
Antonyms: none provided
A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Definition source: English Wiktionary via Wiktextract
Topics: engineering, natural-sciences, physical-sciences, physics
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
Across languages
Translations
33 source translations are retained for this English entry.
-
Asturian:
vector propiu
— vector not rotated by linear transformation
-
Asturian:
autovector
— vector not rotated by linear transformation
-
Catalan:
vector propi
— vector not rotated by linear transformation
-
Chinese Mandarin:
本徵向量 /本征向量
(běnzhēng xiàngliàng)
— vector not rotated by linear transformation
-
Chinese Mandarin:
特徵向量 /特征向量
(tèzhēng xiàngliàng)
— vector not rotated by linear transformation
-
Danish:
egenvektor
— vector not rotated by linear transformation
-
Dutch:
eigenvector
— vector not rotated by linear transformation
-
Estonian:
omavektor
— vector not rotated by linear transformation
-
Finnish:
ominaisvektori
— vector not rotated by linear transformation
-
French:
vecteur propre
— vector not rotated by linear transformation
-
Galician:
vector propio
— vector not rotated by linear transformation
-
Galician:
autovector
— vector not rotated by linear transformation
-
Galician:
eigenvector
— vector not rotated by linear transformation
-
German:
Eigenvektor
— vector not rotated by linear transformation
-
Greek:
ιδιοδιάνυσμα
(idiodiánysma)
— vector not rotated by linear transformation
-
Hebrew:
וֶקְטוֹר עַצְמִי
— vector not rotated by linear transformation
-
Hindi:
अभिलक्षणिक सदिश
(abhilakṣaṇik sadiś)
— vector not rotated by linear transformation
-
Icelandic:
eiginvigur
— vector not rotated by linear transformation
-
Icelandic:
eiginvektor
— vector not rotated by linear transformation
-
Italian:
autovettore
— vector not rotated by linear transformation
-
Japanese:
固有ベクトル
(koyū bekutoru)
— vector not rotated by linear transformation
-
Norwegian Bokmål:
egenvektor
— vector not rotated by linear transformation
-
Norwegian Nynorsk:
eigenvektor
— vector not rotated by linear transformation
-
Polish:
wektor własny
— vector not rotated by linear transformation
-
Portuguese:
autovetor
— vector not rotated by linear transformation
-
Portuguese:
vetor próprio
— vector not rotated by linear transformation
-
Romanian:
vector propriu
— vector not rotated by linear transformation
-
Russian:
со́бственный ве́ктор
(sóbstvennyj véktor)
— vector not rotated by linear transformation
-
Spanish:
vector propio
— vector not rotated by linear transformation
-
Spanish:
autovector
— vector not rotated by linear transformation
-
Spanish:
eigenvector
— vector not rotated by linear transformation
-
Swedish:
egenvektor
— vector not rotated by linear transformation
-
Welsh:
fector eigen
— vector not rotated by linear transformation
