eigenvector
nounEtymology 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.
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Linear algebra, Mathematics, Sciences 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 ).2025 March 22 (last accessed), “Lesson 11”, in University College London, archived from the original on 06 Oct 2021, 8.2 Method to find eigenvalues and eigenvectors, page 1:
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Engineering, Natural sciences, Physical sciences, Physics A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
- Derived terms
- eigenbivector, eigenvectorial, left eigenvector, right eigenvector
- Related terms
- eigenbasis, eigenbrain, eigendecomposition, eigenface, eigenfunction, eigenhead, eigenmode, eigenpair, eigenspace, eigenspinor, eigenstate, eigensystem, eigentheory, eigenvalue, Mathworld article on eigenvectors