wikipedia
English
Etymology
From G. eigen, �own� + value.
Pronunciation
enPR|īʹg�n'v�lyo�o, IPA|/�aɪg�n�vælju�/
audio|en-us-eigenvalue.ogg|Audio (US)
Noun
en-noun
- linearalg The change in magnitude of a vector that is not rotated under a given linear transformation; formally, a scalar <math>\lambda</math> such that, for a particular matrix <math>A</math>, <math>A x \lambda x</math> for some nonzero vector <math>x</math>, an eigenvector of the matrix; thus, a value of <math>\lambda</math> such that <math>\mathrm{det}(A - \lambda I) 0</math> for a given square matrix <math>A</math>, where <math>I</math> is the identity matrix and <math>\mathrm{det}</math> is the determinant operator.
Usage notes
While there is a distinction between left and right eigenvectors, no such distinction is necessary for eigenvalues.
Synonyms
characteristic root, characteristic value, eigenroot, latent value
Related terms
eigen decomposition
eigenfunction
eigenvector
Translations
trans-top|specific value related to a matrix
Czech: vlastnà hodnota f
Dutch: t-|nl|eigenwaarde|f
German: t+|de|Eigenwert|m
Finnish: ominaisarvo
French: valeur propre f
Icelandic: t-|is|eigingildi|n
Italian: t+|it|autovalore|m
trans-mid
Japanese: JAchar|��� (koyūchi)
Portuguese: valor próprio m
Romanian: valoare proprie f
Russian: �об��венное зна�ение (sóbstvennoje zna�énije) n
Slovak: vlastná hodnota f
Swedish: t+|sv|egenvärde|n
Spanish: autovalor m, valor propio m, valor caracterÃstico m (dated)
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See also
Mathworld article on eigenvalues
fr:eigenvalue
pt:eigenvalue
sv:eigenvalue
vi:eigenvalue
zh:eigenvalue
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