Editing on Linux.....
If your looking for a full blown NLE cheap or free then your probably not going to get very far. There are a few open source projects but none proven reliable enough for the mainstream.
If your looking for professional products on Linux in the video realm, then these are abundant. Companies like us (SpectSoft), Autodesk, Max-T and many more offer solutions that in the workforce everyday, all on Linux. These are designed for the strenuous requirements of the industry and unfortunately are not free.
Here is a link to a friend who has the scoop on both sides of this.
http://www.linuxmovies.org/software.html
We have a editor in the works but have have not decided if it will be released as free standalone product along side being a feature in our Rave product or just part of Rave alone.
Cheers,
Ramona