# xorbits.numpy.linalg.eigvalsh#

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

Return type

(…, M,) ndarray

Raises

LinAlgError – If the eigenvalue computation does not converge.

`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

New in version 1.8.0(numpy.linalg).

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

Warning

This method has not been implemented yet. Xorbits will try to execute it with numpy.linalg.

This docstring was copied from numpy.linalg.