What does "eigenvector" mean?

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).

What is a synonym for "eigenvector"?

Common synonyms include: characteristic vector, latent vector, latent vector, proper vector.

Eigenvector

noun

noun ·Rare ·Advanced level

Definitions

Noun

1
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 )."
2
A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."

Synonyms

All synonyms

characteristic vector latent vector latent vector proper vector

Example

More examples

"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 )."

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.

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.