eigenvector

English

Etymology

eigen- +‎ vector, a partial calque of German Eigenvektor.

Pronunciation

• Audio (US)

  (file)

Noun

eigenvector (plural eigenvectors)

1. (linear algebra) given a linear transformation $A$, a vector $x$ such that $Ax=\lambda x$ for some scalar $\lambda$
2. (linear algebra) specifically, given a matrix A, the eigenvector of the transformation "left-side multiplication by A"

Synonyms

• latent vector, proper vector
• characteristic vector

Derived terms

• eigenvectorial
• left eigenvector
• right eigenvector

Related terms

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

Translations

vector not rotated by linear transformation

• Chinese:

  Mandarin: 本徵向量／本征向量 (zh) (běnzhēng xiàngliàng), 特徵向量／特征向量 (zh) (tèzhēng xiàngliàng)

• Danish: egenvektor c
• Dutch: eigenvector (nl) m
• Estonian: omavektor
• Finnish: ominaisvektori
• French: vecteur propre (fr) m
• German: Eigenvektor (de) m
• Greek: ιδιοδιάνυσμα (el) n (idiodiánysma)
• Hebrew: וֶקְטוֹר עַצְמִי‎ m
• Icelandic: eiginvigur m, eiginvektor m
• Italian: autovettore (it) m
• Japanese: 固有ベクトル (ja) (koyū bekutoru)
• Norwegian:

  Bokmål: egenvektor m

  Nynorsk: eigenvektor m

• Polish: wektor własny m
• Portuguese: autovetor m, vetor próprio m
• Romanian: vector propriu m
• Russian: со́бственный ве́ктор m (sóbstvennyj véktor)
• Spanish: vector propio m, autovector m
• Swedish: egenvektor (sv) c

See also

• Mathworld article on eigenvectors

Dutch

Etymology

From eigen +‎ vector, calque of German Eigenvektor.

Pronunciation

• IPA^(key): /ˈɛi̯.ɣənˌvɛk.tɔr/

• Audio

  (file)

• Hyphenation: ei‧gen‧vec‧tor

Noun

eigenvector m (plural eigenvectoren)

1. (linear algebra) eigenvector

Spanish

Noun

eigenvector m (plural eigenvectores)

1. (linear algebra) eigenvector

   Synonyms: autovector, vector propio