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How to use eigenvalue in a sentence

15 example sentences · noun

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. Example: “Hermitian matrices have real diagonal elements as well as real eigenvalues.”

Examples of eigenvalue by meaning

nounA scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a...

  • 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.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...
  • 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.2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications, CRC Press (Chapman &...

More sentences with eigenvalue

  • Hermitian matrices have real diagonal elements as well as real eigenvalues.From the entry Hermitian matrix
  • If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal.From the entry Hermitian matrix
  • Remainder estimates for the approximations to the first eigenvalue and associated eigenfield are presented.2016, V. G. Maz'ya, A.B. Movchan, M.J. Nieves, “Eigenvalue problem in a solid with many inclusions: asymptotic analysis”, in arXiv. From the entry eigenfield
  • The eigenvectors of an orthogonal or unitary operator, corresponding to different eigenvalues, are orthogonal.1997, P. K. Suetin, Alexandra I. Kostrikin, Yuri I. Manin, translated by M. E. Alferieff, Linear Algebra and Geometry, page 137. From the entry unitary
  • When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity.2016, Jinyan Fan, Jiawang Nie, Anwa Zhou, “Tensor Eigenvalue Complementarity Problems”, in arXiv. From the entry copositivity
  • In this chapter we extend the study of eigenvalues to Riemannian manifolds whose curvature may not be constant, but is, nevertheless, bounded.1984, Isaac Chavel, Eigenvalues in Riemannian Geometry, Academic Press, page 55. From the entry Riemannian manifold
  • From this Coulomb function, we can then calculate the logarithmic derivative of U²(r) at the eigenvalue for any value of r outside the core.1955, Frank S. Ham, “The Quantum Defect Method”, in Frederick Seitz, David Turnbull, editors, Solid State Physics, Volume 1, Academic…. From the entry logarithmic derivative
  • The purpose of this section is to introduce the basic terms and concepts connected with eigentheory: eigenvalues, eigenvectors, eigenpairs, eigenspaces, the characteristic polynomial, and the characteristic equation.2017, James B. Carrell, Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra, Springer, page 239. From the entry eigentheory
  • Then we define the Krein signature of the eigenvalues of modulus one of a symplectic matrix and use this concept to build the rotation function on the symplectic group.2001, Alberto Abbondandolo, Morse Theory for Hamiltonian Systems, CRC Press (Chapman & Hall/CRC), page x. From the entry symplectic matrix
  • For example, in the case of eigenvalue problems (see Chapter 1) corresponding “unreasonabilities” are eminently interesting for engineers, producing “critical values” in buckling problems, and so forth.1999, Karel Rektorys, “Introduction”, in Solving Ordinary and Partial Boundary Value Problems in Science and Engineering, Boca Raton…. From the entry unreasonability
  • As a corollary it follows that an antisymmetric matrix of odd order necessarily has one eigenvalue equal to zero; antisymmetric matrices of odd order are singular.1974, Robert McCredie May, Stability and Complexity in Model Ecosystems, Princeton University Press, page 193. From the entry antisymmetric
  • In the previous chapter algorithms for computing the eigenvalues of symplectic matrices have been considered that are based on an elimination process for computing the butterfly form of symplectic matrix.2002, Heike Fassbender, Symplectic Methods for the Symplectic Eigenproblem, Kluwer Academic, page 173. From the entry symplectic matrix

Meaning of eigenvalue

  1. 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.

Full definition of eigenvalue

Questions about eigenvalue in a sentence

How do you use eigenvalue in a sentence?
Eigenvalue is used as a noun. For example: “Hermitian matrices have real diagonal elements as well as real eigenvalues.”
What is a short sentence with eigenvalue?
“Hermitian matrices have real diagonal elements as well as real eigenvalues.”
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.

Source and license

Adapted from Wiktionary: eigenvalue (page history and authors) and the entries each sentence comes from. Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws chose the sentences, left out offensive ones and quotations older than 1900, and marked the word in each. Wiktionary data of 2026-09-02.

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