Implement Eigendecomposition

[mofeing]

This PR implements LinearAlgebra.eigen (and related methods, eigvals and eigvecs) for Tensor, and LinearAlgebra.eigen! for AbstractTensorNetwork.

The design of this implementation is somewhat more similar to how Julia implements factorizations: there is this new TensorEigen object which eigen(::Tensor) returns. We could have used LinearAlgebra.Eigen (which is the return type of eigen), but it doesn't store the right indices required to construct $U^{-1}$.

The following destructuring syntax is supported:

A = Tensor(normalize!(rand(2,2)), [:i, :j])

Λ, U = eigen(A)
(; U⁻¹) = eigen(A)
(; Uinv) = eigen(A)
(; U, Λ, U⁻¹) = eigen(A)

[jofrevalles]

Okay thanks! Can you add tests for this? See our test for KrylovKit.eigsolve, which may be very similar.

Also, we should make that both KrylovKit.eigsolve and this function you added should have similar syntax, so if we agree on this TensorEigen thing, we should add it to our KrylovKit extension.

[mofeing]

Okay thanks! Can you add tests for this? See our test for KrylovKit.eigsolve, which may be very similar.

Sure

Also, we should make that both KrylovKit.eigsolve and this function you added should have similar syntax, so if we agree on this TensorEigen thing, we should add it to our KrylovKit extension.

mmm although it might be a good idea, I see that Krylovkit.eigsolve doesn't return a Factorization object like LinearAlgebra.eigen so I would prefer to leave that for another PR.

[mofeing]

Nice! Can you add a docstring? :)

Done!