eigenvalue

Etymology
, a.

Noun

 * 1)  A scalar, $$\lambda$$, such that there exists a non-zero vector $$x$$ (a corresponding eigenvector) for which the image of $$x$$ under a given linear operator $$\mathrm{A}$$ is equal to the image of $$x$$ under multiplication by $$\lambda$$; i.e. $$\mathrm{A} x = \lambda x$$.

Usage notes

 * When unqualified, as in the above example, eigenvalue conventionally refers to a right eigenvalue, characterised by $$\mathrm{M} x = \lambda x$$ for some right eigenvector $$x$$. Left eigenvalues, characterised by $$y \mathrm{M} = y\lambda$$ also exist with associated left eigenvectors $$y$$. (In consequence of the equations, 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: ,
 * Czech: vlastní hodnota
 * Danish: egenværdi
 * Dutch:
 * Estonian: omaväärtus
 * Finnish: ominaisarvo
 * French:
 * German:
 * Greek:
 * Hebrew: עֵרֶךְ עַצְמִי
 * Icelandic: eigingildi
 * Italian:
 * Japanese:
 * Lithuanian: tikrinė reikšmė
 * Norwegian:
 * Bokmål: egenverdi
 * Nynorsk: eigenverdi
 * Persian: مقدار ویژه
 * Polish:
 * Portuguese: valor próprio, autovalor
 * Romanian: valoare proprie
 * Russian: со́бственное значе́ние
 * Slovak: vlastná hodnota
 * Spanish: autovalor, valor propio, valor característico
 * Swedish: