* `linalg.eig` always returns complex dtype

* Update Eig dispatch for Numba, Jax, and Pytorch backends

* Clean up `pytensor.linalg.expm` and related tests

* Add JAX dispatch for expm

* Implement L_op instead of grad in `Eigh`

---------
Co-authored-by: Jesse Grabowski <jesse.grabowski@readyx.com>

This isn't strictly needed but it's a more intuitive placement

Helpers before dispatchers

They are actually defined in tensor/math.py, but this is better than being in `basic.py`

It seems that libiomp5.lib has been renamed to libiomp5md.lib, so the detection was failing.
Add another search step with the new library name.

TODO: is there a more modern approach?
Co-authored-by: Luciano Paz <luciano.paz.neuro@gmail.com>

* Delete `sparse.sandbox`

* delete test_sp2.py

```bash
uvx gha-tools autoupdate ./.github/workflows/ --pin=all --version-strategy=specific --write
```

Calling `lru_cache` on instance methods causes a leak. Fixed as suggested in https://rednafi.com/python/lru-cache-on-methods/

* Initial plan

* Fix issue #1554: Preserve custom thumbnails in gallery script

Modified scripts/generate_gallery.py to check if a thumbnail file already
exists before extracting from notebooks. This prevents the script from
overwriting manually-placed custom thumbnails in the _thumbnails directory.

The gen_previews() method now:
1. Checks if self.png_path exists
2. If yes, logs info message and returns early (preserving custom thumbnail)
3. If no, proceeds with extraction from notebook or uses default logo

Fixes #1554

---------
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>

* Use lapack instead of `scipy_linalg.cho_solve`

* Use lapack instead of `scipy_linalg.lu_factor`

* Use lapack instead of `scipy_linalg.solve_triangular`

* Add empty test for lu_factor

* Tidy imports

* remove ndim check

Pre-commit will not install hooks by default, and Copilot has no network access to install afterwards. Pre-install during setup

Co-authored-by: ricardoV94 <28983449+ricardoV94@users.noreply.github.com>

Co-authored-by: Carlos Trujillo <59846724+cetagostini@users.noreply.github.com>
Co-authored-by: Ricardo Vieira <28983449+ricardoV94@users.noreply.github.com>
Co-authored-by: Jesse Grabowski <48652735+jessegrabowski@users.noreply.github.com>

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: ricardoV94 <28983449+ricardoV94@users.noreply.github.com>