Sue,
I have an idea that might work for that larger space. You can't mat a stretched canvas, you have to build a flat box frame and cover it to serve as a 'mat' than add a frame to the outer edges of that. So unless you know exactly what to do, it shouldn't be done.
Oh BUT . . . here's my other idea that could be a possibility. Hang the painting where you want it. Find a wide frame that has a much bigger opening than the painting is, and is flush against the wall. Center the frame over the painting and hang it around it, the wall color will show in the space around the painting and will serve to look like a 'mat' for the painting.
Might work. And would take up some of that extra space.