Definition of eigenvalue in English:



Physics Mathematics
  • 1Each of a set of values of a parameter for which a differential equation has a nonzero solution (an eigenfunction) under given conditions.

    • ‘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.’
    • ‘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 a zero determinant.

    • ‘In general, it is difficult to calculate the eigenvalues.’
    • ‘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.’
    • ‘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.’