Possible? Yes. Easy? That depends.
You can do it with software, but the majority of the software I know of isn't free... that being said, I'd bet free software out there will do that...
I'd look for alternatives to something like adobe after effects or premier.... there's one I'm thinking of... I think it beings with the letter "O" and has a blue logo... I've used that on Ubuntu and I think it had the option to do that.
The process you want to do is to use either the left/right or top/bottom half right?
(just so I understand).
What software you use will depend on the OS you are running... Actually, you *might* be able to do that in Windows Movie Maker....
Hope that helps.