eigenvalue
Pronunciation Noun
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Pronunciation Noun
eigenvalue (plural eigenvalues)
- (linear algebra) A scalar, \lambda, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator \mathrm{A} is equal to the image of x under multiplication by \lambda; i.e. \mathrm{A} x = \lambda x.
- The eigenvalues \lambda of a square transformation matrix \mathrm{M} may be found by solving \det(\mathrm{M} - \lambda\mathrm{I}) = 0.
- 1972, Frederick Valentine Atkinson, Multiparameter Eigenvalue Problems, Volume I: Matrices and Compact Operators, Academic Press, page x ↗,
- 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 l920's by R. D. Carmichael, who pointed out in addition the enormous variety of mixed eigenvalue problems with several parameters.
- 2000, Hinne Hettema (translator), J. Von Neumann, Eugene Wigner, On the Behaviour of Eigenvalues in Adiabatic Processes [1929], Hinne Hettema (editor), Quantum Chemistry: Classic Scientific Papers, World Scientific, page 25 ↗,
- 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 region in between is particularly interesting.
- 2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications, CRC Press (Chapman & Hall), page 1 ↗,
- Problems that require an investigation of eigenvalues and eigenfunctions arise in connection with numerous topics in mechanics, the theory of vibrations and stability, hydrodynamics, elasticity, acoustics, electrodynamics, quantum mechanics, etc.
- (scalar multiplier of an eigenvector) characteristic root, characteristic value, eigenroot, latent value, proper value
- French: valeur propre
- German: Eigenwert
- Italian: autovalore
- Portuguese: valor próprio, autovalor
- Russian: со́бственное значе́ние
- Spanish: autovalor, valor propio, valor característico m (dated)
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003