eigenvector
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English
Etymology
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.
Pronunciation
Noun
eigenvector (plural eigenvectors)
- (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 for some scalar λ (called the eigenvalue).
- Synonyms: characteristic vector, latent vector, proper vector
- (physics, engineering) 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 of linear 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.
Derived terms
Related terms
- eigenbasis
- eigenbrain
- eigendecomposition
- eigenface
- eigenfunction
- eigenhead
- eigenmode
- eigenpair
- eigenspace
- eigenspinor
- eigenstate
- eigensystem
- eigentheory
- eigenvalue
Translations
vector not rotated by linear transformation
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See also
Dutch
Etymology
From eigen + vector, calque of German Eigenvektor.
Pronunciation
Noun
eigenvector m (plural eigenvectoren)
Spanish
Noun
eigenvector m (plural eigenvectores)
- (linear algebra) eigenvector
- Synonyms: autovector, vector propio