Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun A vector whose direction is unchanged by a given transformation and whose magnitude is changed by a factor corresponding to that vector's eigenvalue. In quantum mechanics, the transformations involved are operators corresponding to a physical system's observables. The eigenvectors correspond to possible states of the system, and the eigenvalues to possible observed values.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun linear algebra A vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.
  • noun physics, engineering A right eigenvector; a nonzero vector such that, for a particular matrix , for some scalar which is its eigenvalue and an eigenvalue of the matrix.

Etymologies

from The American Heritage® Dictionary of the English Language, 4th Edition

[Partial translation of German Eigenvektor : eigen-, characteristic; see eigenvalue + Vektor, vector.]

from Wiktionary, Creative Commons Attribution/Share-Alike License

eigen- +‎ vector

Examples

Comments

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  • eigenvector: There was a time when I knew what this word meant -- just enough to know I'd never really be able to use one.

    December 7, 2006