eig_op

→std::vector<TensorImplPtr>

int eig_op(const int & a)

source edit

Python wrappers

pylucid.linalg.eigfunction

Compute eigenvalues and right eigenvectors of a square float matrix.

Math

Returns $(w, V)$ such that $A V = V \mathrm{diag}(w)$ , equivalently $A v_i = w_i v_i$ for each column $v_i$ of $V$ .

Shape

Input a : (..., n, n)
Output w : (..., n)
Output V : (..., n, n)

See Also

[[eigh_op]] : Symmetric / Hermitian specialisation (preferred when applicable — faster, real outputs, autograd-friendly).

Parameters

aconst TensorImplPtr&

Square float tensor of shape (..., n, n). Leading dimensions are treated as independent batch axes — one decomposition per batch element. Must be at least 2-D and floating-point.

Returns

std::vector<TensorImplPtr>

Two-element vector {w, V} where: - w has shape (..., n) — one eigenvalue per column of $A$ (real part only; see Notes on complex spectra). - V has shape (..., n, n) — columns are the right eigenvectors, normalised to unit Euclidean length.

Raises

LinAlgError

When a is not at least 2-D, not square, or not float-typed. Also if LAPACK fails to converge (rare; reported via info > 0).

Notes

Outputs are leaf nodes — autograd is not wired. See header-level Notes for the deferred backward formula and its caveats.

Examples

In Python (via [[lucid.linalg.eig]]):
>>> A = lucid.tensor([[2.0, 0.0], [0.0, 3.0]])
>>> w, V = lucid.linalg.eig(A)
>>> w
Tensor([2., 3.])