Skip to main content
`Ctrl`+`K`

# numpy.linalg.eigvalsh

linalg.eigvalsh(a, UPLO='L')

  Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

  Main difference from eigh: the eigenvectors are not computed.

  Parameters:
    a(…, M, M) array_like

      A complex- or real-valued matrix whose eigenvalues are to be computed.

    UPLO{‘L’, ‘U’}, optional

      Specifies whether the calculation is done with the lower triangular part of a (‘L’, default) or the upper triangular part (‘U’). Irrespective of this value only the real parts of the diagonal will be considered in the computation to preserve the notion of a Hermitian matrix. It therefore follows that the imaginary part of the diagonal will always be treated as zero.

  Returns:
    w(…, M,) ndarray

      The eigenvalues in ascending order, each repeated according to its multiplicity.

  Raises:
    LinAlgError

      If the eigenvalue computation does not converge.

  See also

  `eigh`

    eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays.

  `eigvals`

    eigenvalues of general real or complex arrays.

  `eig`

    eigenvalues and right eigenvectors of general real or complex arrays.

  `scipy.linalg.eigvalsh`

    Similar function in SciPy.

  Notes

  Broadcasting rules apply, see the `numpy.linalg` documentation for details.

  The eigenvalues are computed using LAPACK routines `_syevd`, `_heevd`.

  Examples

      >>> import numpy as np
      >>> from numpy import linalg as LA
      >>> a = np.array([[1, -2j], [2j, 5]])
      >>> LA.eigvalsh(a)
      array([ 0.17157288,  5.82842712]) # may vary

      >>> # demonstrate the treatment of the imaginary part of the diagonal
      >>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
      >>> a
      array([[5.+2.j, 9.-2.j],
             [0.+2.j, 2.-1.j]])
      >>> # with UPLO='L' this is numerically equivalent to using LA.eigvals()
      >>> # with:
      >>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
      >>> b
      array([[5.+0.j, 0.-2.j],
             [0.+2.j, 2.+0.j]])
      >>> wa = LA.eigvalsh(a)
      >>> wb = LA.eigvals(b)
      >>> wa
      array([1., 6.])
      >>> wb
      array([6.+0.j, 1.+0.j])