Action of the matrix exponential on vectors
Hi @ivanZanardi ,

Thanks for the request. Could you please confirm whether this feature available in any other libraries like numpy,scipy,Jax etc? Hi @SuryanarayanaY,

Thanks for getting back to me. Yes, the implementation of the referenced algorithm can be found in SciPy's [`scipy.sparse.linalg.expm_multiply`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.expm_multiply.html) function.

Thanks,
Ivan Any updates on this?

Thanks,
Ivan
### Issue type

Feature Request

### Have you reproduced the bug with TensorFlow Nightly?

No

### Source

source

### TensorFlow version

2.10.0

### Custom code

No

### OS platform and distribution

_No response_

### Mobile device

_No response_

### Python version

_No response_

### Bazel version

_No response_

### GCC/compiler version

_No response_

### CUDA/cuDNN version

_No response_

### GPU model and memory

_No response_

### Current behavior?

Hello everyone,

I was wondering if there are any plans to implement the **action of the matrix exponential on vectors** in the codebase. This targeted computation, rather than the full matrix exponential (`tf.linalg.expm`), would greatly benefit users, especially those using exponential-based integrators.

References:
- SIAM Paper: [Link](https://doi.org/10.1137/100788860)
- MATLAB Code: [GitHub](https://github.com/higham/expmv)

Thanks for considering!
Ivan

### Standalone code to reproduce the issue

```shell
n/a
```


### Relevant log output

_No response_