noun

• 1Each of a set of values of a parameter for which a differential equation has a non-zero solution (an eigenfunction) under given conditions.

  ‘He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions.’

  More example sentences

  • ‘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.’
  • ‘Then they sorted the eigenvectors according to the eigenvalues and divided them into three subsets.’
  • ‘Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates.’

• 2Any number such that a given matrix minus that number times the identity matrix has zero determinant.

  ‘In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.’

  More example sentences

  • ‘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.’
  • ‘There is, however, a way to obtain the kinetic matrix from the experimental eigenvalues and the eigenvectors directly.’
  • ‘In general, it is difficult to calculate the eigenvalues.’