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Definition eigenvalue

Etymology

eigen- +‎ value, a partial translation of German Eigenwert.

Noun

eigenvalue (plural eigenvalues)

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