# jax.numpy.linalg.eigh#

jax.numpy.linalg.eigh(a, UPLO=None, symmetrize_input=True)[source]#

Return the eigenvalues and eigenvectors of a complex Hermitian

LAX-backend implementation of `numpy.linalg.eigh()`.

Original docstring below.

(conjugate symmetric) or a real symmetric matrix.

Returns two objects, a 1-D array containing the eigenvalues of a, and a 2-D square array or matrix (depending on the input type) of the corresponding eigenvectors (in columns).

Parameters:
• a ((..., M, M) array) â€“ Hermitian or real symmetric matrices whose eigenvalues and eigenvectors are to be computed.

• UPLO ({'L', 'U'}, optional) â€“ Specifies whether the calculation is done with the lower triangular part of a (â€˜Lâ€™, default) or the upper triangular part (â€˜Uâ€™). 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.

Return type:

EighResult

Returns:

• A namedtuple with the following attributes

• eigenvalues ((â€¦, M) ndarray) â€“ The eigenvalues in ascending order, each repeated according to its multiplicity.

• eigenvectors ({(â€¦, M, M) ndarray, (â€¦, M, M) matrix}) â€“ The column `eigenvectors[:, i]` is the normalized eigenvector corresponding to the eigenvalue `eigenvalues[i]`. Will return a matrix object if a is a matrix object.

References

Parameters:

symmetrize_input (bool) â€“