mlx.core.linalg.eig

eig(a: array, *, stream: None | Stream | Device = None) → Tuple[array, array]

Compute the eigenvalues and eigenvectors of a square matrix.

This function differs from numpy.linalg.eig() in that the return type is always complex even if the eigenvalues are all real.

This function supports arrays with at least 2 dimensions. When the input has more than two dimensions, the eigenvalues and eigenvectors are computed for each matrix in the last two dimensions.

Parameters:

• a (array) – The input array.

• stream (Stream, optional) – Stream or device. Defaults to None in which case the default stream of the default device is used.

Returns:

A tuple containing the eigenvalues and the normalized right eigenvectors. The column v[:, i] is the eigenvector corresponding to the i-th eigenvalue.

Return type:

Tuple[array, array]

Example

>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> w, v = mx.linalg.eig(A, stream=mx.cpu)
>>> w
array([3+0j, -1+0j], dtype=complex64)
>>> v
array([[0.707107+0j, 0.707107+0j],
       [-0.707107+0j, 0.707107+0j]], dtype=complex64)