Many programmers don't understand matrices either. If you're going to be working with 3D engines, some of this stuff you'll just have to sit down and learn.
Also, it is not really interesting what matrices or quaternions "can do". What is interesting is what we can do with them. And quaternions make a lot of things possible that are intractable or at least a huge pain with matrices.
Yes, that was my point, that what you can do with quats is a strict subset of what you can do with 4x4 mats. Not sure what you thought I meant.
> quaternions make a lot of things possible that are intractable
Such as?