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

Recent Examples on the Web 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

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'eigenvalue.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History


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

Dictionary Entries Near eigenvalue

Cite this Entry

“Eigenvalue.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/eigenvalue. Accessed 29 Nov. 2023.

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