# numpy.linalg.eigvalsh¶

`numpy.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. w : (…, M,) ndarray The eigenvalues in ascending order, each repeated according to its multiplicity. 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.

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]) # 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])
```

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