eigenvector

Definitions

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

Equivalents

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 ).”

CEFR level