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.
〔数，物理〕本征值，特征值
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.
本征函数中的一个参数的许多允许值之一
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.
〔数，物理〕本征值，特征值
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.
本征函数中的一个参数的许多允许值之一
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.

词汇	eigenvalue
释义	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. 〔数，物理〕本征值，特征值 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. 本征函数中的一个参数的许多允许值之一 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. 〔数，物理〕本征值，特征值 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. 本征函数中的一个参数的许多允许值之一 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.
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