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# numpy.linalg.eigvalsh

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

  Compute the eigenvalues of a 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 symmetric/Hermitian arrays.
  `eigvals`
    eigenvalues of general real or complex arrays.
  `eig`
    eigenvalues and right eigenvectors of general real or complex arrays.

  Notes

  New in version 1.8.0.

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

  The eigenvalues are computed using LAPACK routines _syevd, _heevd

  Examples

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

      >>> # 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; wb
      array([ 1.,  6.])
      array([ 6.+0.j,  1.+0.j])