eigenvalue

noun

ei·​gen·​val·​ue ˈī-gən-ˌval-(ˌ)yü 

: a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector which when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector

especially : a root of the characteristic equation of a matrix

Examples of eigenvalue in a Sentence

Recent Examples on the Web

Mathematicians measure the size of those changes using numbers called eigenvalues. —Jordana Cepelewicz, WIRED, 4 Aug. 2024

Time and again, regardless of their specific characteristics, the random matrices are found to exhibit that same chaotic yet regular pattern in the distribution of their eigenvalues. —Quanta Magazine, 5 Feb. 2013

The pattern involved a second layer of numbers called eigenvalues, which are like the DNA of a matrix. —Quanta Magazine, 6 May 2019

By contrast, the Tracy-Widom curve appears to arise from variables that are strongly correlated, such as interacting species, stock prices and matrix eigenvalues. —Natalie Wolchover, WIRED, 27 Oct. 2014

Word History

Etymology

partial translation of German Eigenwert, from eigen own, peculiar + Wert value

First Known Use

1927, in the meaning defined above