eigenvector
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).
Noun
- 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).
- Both equations give the relation x₁ = −x₂. Therefore the set of eigenvectors corresponding to λ = 2 is given by: […] An eigenvector corresponding to λ₁ = 2 is ( −1 1 ). - (Can we date this quote?), “Lesson 11”, in...
Synonyms: characteristic vector latent vector proper vector
- A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Origin
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.
Forms
Related
eigenbasis eigenbrain eigendecomposition eigenface eigenfunction eigenhead eigenmode eigenpair eigenspace eigenspinor eigenstate eigensystem eigentheory eigenvalue Mathworld article on eigenvectors
Derived
eigenbivector eigenvectorial left eigenvector right eigenvector