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Add complex number support to eigh and eigvalsh #543

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kgryte committed Dec 1, 2022
commit a74013f7d9c5cf87bd128596a3b410062f5659ab
2 changes: 1 addition & 1 deletion spec/API_specification/array_api/linalg.py
Original file line number Diff line number Diff line change
Expand Up @@ -120,7 +120,7 @@ def eigh(x: array, /) -> Tuple[array]:
.. math::
x = Q \Lambda Q^H

where :math:`Q^H` is the conjugate transpose when :math:`Q` is complex and the transpose when :math:`Q` is real-valued and :math:`\Lambda` is a diagonal matrix whose diagonal elements are the corresponding eigenvalues. When ``x`` is real-valued, :math:`Q` is orthogonal, and, when ``x`` is complex, :math:`Q` is unitary.
with :math:`Q \in \mathbb{K}^{n \times n}` and :math:`\Lambda \in \mathbb{R}^n` and where :math:`Q^H` is the conjugate transpose when :math:`Q` is complex and the transpose when :math:`Q` is real-valued and :math:`\Lambda` is a diagonal matrix whose diagonal elements are the corresponding eigenvalues. When ``x`` is real-valued, :math:`Q` is orthogonal, and, when ``x`` is complex, :math:`Q` is unitary.

.. note::
The eigenvalues of a complex Hermitian or real symmetric matrix are always real.
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