eigenvalue

noun

ei·​gen·​val·​ue ˈī-gən-ˌval-(ˌ)yü How to pronounce eigenvalue (audio)
: 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

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Wigner conjectured that the eigenvalues of any random matrix should always obey the same probability distribution. Leila Sloman, Quanta Magazine, 18 Apr. 2025 Mathematicians measure the size of those changes using numbers called eigenvalues. Jordana Cepelewicz, WIRED, 4 Aug. 2024

Word History

Etymology

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

First Known Use

1927, in the meaning defined above

Time Traveler
The first known use of eigenvalue was in 1927

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Cite this Entry

“Eigenvalue.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/eigenvalue. Accessed 12 Sep. 2025.

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