eigenvalue
Syllables: ei·gen·val·ueUK/ˈaɪ.ɡənˌvæl.juː//ˈaɪ.ɡənˌvæl.ju/
eigenvalue noun: a scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
Noun
eigenvalue (plural eigenvalues)
- A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
- In the extension, one associates eigenvalues, sets of scalars, with arrays of matrices by considering the singularity of linear combinations of the matrices in the various rows, involving the same coefficients in each case. Attention to this area was called in the early 1920's by R. D. Carmichael...1972, F. V. Atkinson, Multiparameter Eigenvalue Problems, Volume I: Matrices and Compact Operators, Academic Press, page x
- For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the...2000, John von Neumann, E. Wigner, “On the Behaviour of Eigenvalues in Adiabatic Processes”, in Hinne Hettema, transl., edited by Hinne Hettema, Quantum Chemistry: Classic Scientific Papers, World...
- Synonyms:
- characteristic root, characteristic value, eigenroot, latent value, proper value
eigenvalue meaning in Hindi and Persian
eigenvalue in Hindi
- scalar multiplier of an eigenvector
- अभिलाक्षणिक मान abhilākṣaṇik mān
eigenvalue in Persian
- scalar multiplier of an eigenvector
- مقدار ویژه meqdâr-e viže
Examples of eigenvalue in a sentence
- Carmichael, who pointed out in addition the enormous variety of mixed eigenvalue problems with several parameters.1972, F. V. Atkinson, Multiparameter Eigenvalue Problems, Volume I: Matrices and Compact Operators, Academic Press, page x:
- For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters.2000, John von Neumann, E. Wigner, “On the Behaviour of Eigenvalues in Adiabatic Processes”, in Hinne Hettema, transl., edited by Hinne...
- To find all the eigenvalues of A, solve the characteristic equation. ¶ For each eigenvalue λ, to find the corresponding set of eigenvectors, solve the linear system of equations […]2025 March 22 (last accessed), “Lesson 12”, in University College London, archived from the original on 21 Mar 2025, page 1:
Synonyms of eigenvalue
Forms of eigenvalue
| plural | eigenvalues |
|---|
Origin of eigenvalue
From eigen- + value. Partial calque of German Eigenwert.
Words formed from eigenvalue
Questions about eigenvalue
- What does eigenvalue mean?
- Eigenvalue means a scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
- What is eigenvalue in Hindi?
- Eigenvalue in Hindi is अभिलाक्षणिक मान (abhilākṣaṇik mān). See Eigenvalue meaning in Hindi.
- How do you use eigenvalue in a sentence?
- Carmichael, who pointed out in addition the enormous variety of mixed eigenvalue problems with several parameters.
- What part of speech is eigenvalue?
- Eigenvalue is a noun.
- How do you pronounce eigenvalue?
- Eigenvalue is pronounced /ˈaɪ.ɡənˌvæl.juː/ (UK).
- What is the plural of eigenvalue?
- The plural of eigenvalue is eigenvalues.
Words near eigenvalue in the dictionary
Source and license
Adapted from Wiktionary: eigenvalue (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Pronunciation audio from Wikimedia Commons, each file under its own free license: en-us-eigenvalue.ogg.
Cite this entry: “eigenvalue.” Word.ws, https://word.ws/eigenvalue. Based on Wiktionary, CC BY-SA 4.0.