# eigenvalue

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

## Definition of eigenvalue in English:

### noun

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.
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.
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.

## Definition of eigenvalue in:

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