Definition of eigenvalue in English:


Syllabification: ei·gen·val·ue
Pronunciation: /ˈīgənˌvalyo͞o


Mathematics & Physics
  • 1Each of a set of values of a parameter for which a differential equation has a nonzero solution (an eigenfunction) under given conditions.
    More example sentences
    • He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions.
    • It was a matter of estimating eigenvalues of non-self-adjoint differential equations and matrices.
    • In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear.
  • 2Any number such that a given matrix minus that number times the identity matrix has a zero determinant.
    More example sentences
    • In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.
    • This is where those eigenvalues of random Hermitian matrices enter the picture.
    • The eigenvalue effective population size, equal to the leading eigenvalue of this matrix is derived.

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Pronunciation: ˌkɒlərəˈtjʊərə
elaborate ornamentation of a vocal melody