English Explanatory Dictionary

eigenvector

English dictionary entry

Meanings

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

Pronunciation

en-us-eigenvector.ogg

Word forms

eigenvector eigenvectors

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.

Synonyms

characteristic vector latent vector proper vector

Related words

eigenbasis eigenbrain eigendecomposition eigenface eigenfunction eigenhead eigenmode eigenpair eigenspace eigenspinor eigenstate eigensystem eigentheory eigenvalue Mathworld article on eigenvectors

Derived words

eigenbivector eigenvectorial left eigenvector right eigenvector
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