numpy.linalg.eigvalsh#

linalg.eigvalsh(a, UPLO='L')[source]#

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])