Today it means: 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). Full definition →
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.
Etymology from Wiktionary, CC BY-SA 4.0.