eigenvector
noun
eigenvector is a noun meaning “A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on…” (English Wiktionary, September 2026). It is spelled E-I-G-E-N-V-E-C-T-O-R, and it appears about once in every 11 million words in written English (wordfreq, 2021 data). The plural of eigenvector is eigenvectors.
What does eigenvector mean?
noun
- 1
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).
- 2
A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
How do you pronounce eigenvector?
- US
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Recordings: En-us-eigenvector.ogg, Wikimedia Commons (author and licence on each file's page).
Forms of eigenvector
- eigenvectors plural
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
How common is eigenvector?
Eigenvector appears about once in every 11 million words in written English, the 101,613th most frequent word form in the list.
Source: written frequency: wordfreq 3.1 (a 2021 snapshot of Wikipedia, subtitles, news, books, web text and social media).
Eigenvector in Spanish, French, German and Portuguese
In the sense vector not rotated by linear transformation:
| Language | Words |
|---|---|
| French | vecteur propre |
| German | Eigenvektor |
| Portuguese | autovetor, vetor próprio |
| Spanish | vector propio, autovector, eigenvector |
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Translations are Wiktionary's, by sense; a linked word has its own PlainSpell page.
Where does eigenvector come from?
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.
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).