jax.lax.linalg.eigh

jax.lax.linalg.eigh(x, lower=True, symmetrize_input=True)

Eigendecomposition of a Hermitian matrix.

Computes the eigenvalues and eigenvectors of a complex Hermitian or real symmetric square matrix.

Parameters

• x – A batch of square complex Hermitian or real symmetric matrices with shape [..., n, n].

• lower (bool) – If symmetrize_input is False, describes which triangle of the input matrix to use. If symmetrize_input is False, only the triangle given by lower is accessed; the other triangle is ignored and not accessed.

• symmetrize_input (bool) – If True, the matrix is symmetrized before the eigendecomposition by computing \(\frac{1}{2}(x + x^H)\).

Returns

A tuple (v, w).

v is an array with the same dtype as x (or its real counterpart if complex) with shape [..., n] containing the eigenvalues of x.

w is an array with the same dtype as x such that w[..., :, i] is the eigenvector corresponding to v[..., i].