| Definitions | | eigenvalue |
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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.
Translations: - Dutch: eigenwaarde(nl)f
- German: Eigenwert(de)m
- French: valeur propre
- Italian: autovalore(it)m
- Spanish: autovalor , valor propio , valor característico (dated)
Etymology: From eigen, "own" + value.
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