eigenvector

Etymology
, a.

The prefix (also used in ) was first used in 1904, by, and was possibly inspired by a related usage by.

Noun

 * 1)  A vector that is not rotated under a particular linear transformation; a left or right eigenvector depending on context;  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."
 * 1)  A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."

Usage notes

 * Eigenvector has become the standard term in English, but was formerly more common.
 * The concepts of eigenvector and eigenvalue arose from the study of quadratic forms and differential equations. Nowadays, they are normally introduced in the context of linear algebra.
 * A linear transformation can always be represented as a matrix if the vector space is finite-dimensional (usually a safe assumption in physics).
 * In consequence of the rules of matrix multiplication, left eigenvectors are row vectors, while right eigenvectors are column vectors. The convention of right eigenvector as "standard" is fundamentally an arbitrary choice.

Translations

 * Chinese:
 * Mandarin: ,
 * Danish: egenvektor
 * Dutch:
 * Estonian: omavektor
 * Finnish: ominaisvektori
 * French:
 * German:
 * Greek:
 * Hebrew: וֶקְטוֹר עַצְמִי
 * Icelandic: eiginvigur, eiginvektor
 * Italian:
 * Japanese:
 * Norwegian:
 * Bokmål: egenvektor
 * Nynorsk: eigenvektor
 * Polish:
 * Portuguese: autovetor, vetor próprio
 * Romanian: vector propriu
 * Russian: со́бственный ве́ктор
 * Spanish: vector propio, autovector
 * Swedish:

Etymology
From,.