Definition of eigenvalue in English:
eigenvalue
nounˈʌɪɡənˌvaljuːˈaɪɡənˌvælju
Mathematics Physics 1Each of a set of values of a parameter for which a differential equation has a non-zero solution (an eigenfunction) under given conditions.
Example sentencesExamples
- In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear.
- It was a matter of estimating eigenvalues of non-self-adjoint differential equations and matrices.
- He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions.
- Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates.
- Then they sorted the eigenvectors according to the eigenvalues and divided them into three subsets.
2Any number such that a given matrix minus that number times the identity matrix has zero determinant.
Example sentencesExamples
- In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.
- In general, it is difficult to calculate the eigenvalues.
- The eigenvalue effective population size, equal to the leading eigenvalue of this matrix is derived.
- There is, however, a way to obtain the kinetic matrix from the experimental eigenvalues and the eigenvectors directly.
- This is where those eigenvalues of random Hermitian matrices enter the picture.
Definition of eigenvalue in US English:
eigenvalue
nounˈaɪɡənˌvæljuˈīɡənˌvalyo͞o
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 sentencesExamples
- Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates.
- It was a matter of estimating eigenvalues of non-self-adjoint differential equations and matrices.
- Then they sorted the eigenvectors according to the eigenvalues and divided them into three subsets.
- In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear.
- He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions.
2Any number such that a given matrix minus that number times the identity matrix has zero determinant.
Example sentencesExamples
- In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.
- The eigenvalue effective population size, equal to the leading eigenvalue of this matrix is derived.
- In general, it is difficult to calculate the eigenvalues.
- This is where those eigenvalues of random Hermitian matrices enter the picture.
- There is, however, a way to obtain the kinetic matrix from the experimental eigenvalues and the eigenvectors directly.