Eigenvector
/ˈaɪɡənˌvɛktər/ei·gen·vec·tornoun
Definition
1.[in linear algebra] a non-zero vector whose direction is unchanged by a given linear map, so the map merely rescales it by a constant factor.
The covariance matrix's leading eigenvector points along the axis of greatest spread in the data.
Formal statement
A v = lambda v, v != 0lambda is the eigenvalue: the factor by which the map stretches that direction.
Etymology
A partial calque of German Eigenvektor, from eigen 'own, characteristic'. Hilbert used Eigenwert in 1904; the hybrid German-English form settled into English mathematics in the 1920s–30s.
Synonyms
- characteristic vectorsense 1 · Absolute
- proper vectorsense 1 · Near
See also
References
- Strang, G. (2016). Introduction to Linear Algebra, 5th ed., ch. 6.Wellesley-Cambridge Press.