Matrix math nodes

Would it be possible to make nodes that can compose, multiply and invert matrices? This would come very handy to orient vectors to orientation frames. A use case would be the need for vectors or 3D noise to follow a deformed surface orientation rather than the world space. Currently, the specialised node "Deform Curves on Surface" does exactly this, but it would be useful to be able to manipulate other types of objects that way. One example I have been attempting to achieve has been a proximity deformer, similar to the "mesh deform". This type of node might involve the creation of an entirely new socket type and might require a lot more consideration. But I am making this proposition to hopefully get a conversation started in this regard. There is a real need for this type of manipulation and maybe there are solutions that could be implemented?