# eigenvector

## English

### Etymology

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.

### Pronunciation

•  Audio (US) (file)

### Noun

English Wikipedia has an article on:
Wikipedia

eigenvector (plural eigenvectors)

1. (linear algebra) A vector that is not rotated 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."

#### Usage notes

• Eigenvector has become the standard term in English, but proper vector was formerly more common.
• The concepts of eigenvector and eigenvalue arose from the study of quadratic forms and differential equations. Nowadays, they are normally introduced in the context oflinear algebra.
• A linear transformation can always be represented as a matrix if the vector space is finite-dimensional (usually a safe assumption in physics).
• In consequence of the rules of matrix multiplication, left eigenvectors are row vectors, while right eigenvectors are column vectors. The convention of right eigenvector as "standard" is fundamentally an arbitrary choice.

## 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