Every now and them somebody brings this up in the dojo and most of the time I'm either the only lefty or there's only one other. Also, if your dominant leg is different to your hand or if being a lefty has affected your training post about that too.
Guess The only way its effected my training is because I'm left leg dominant and I'm a grappler I stand left leg forward. It means when I go back to mma learning to fight from a southpaw stance, and more importantly becoming comfortable shooting off my right leg, is going to be something to overcome. I would have that problem if I was right handed too however.
I'm right handed. But i fight left foot forward mostly. I feel that my right leg keeps beter balance and my left has better technique and flexibility.
Some people have a clear lead hand but can still do a few things with the other one almost/just as well. In my opinion, they're not ambidextrous (so I say fully ambidextrous people are the ones who work with both pretty much evenly).
I was ambidextrous as a kid but the teachers in my public schools forced any ambidextrous kids to choose one over the other for writing and that pretty much sealed me as a righty. That said I do train southpaw a bunch because I like being able to mess people up and fight mirrored sometimes. Also if you just start doing more things with your left hand like brushing your teeth, combing your hair, shaving, eating, you co-ordination with your left hand will increase more than just working the left side in martial arts class.
I'm kind of in between. My dominant hand for writing has always been the left one, while for most other things I prefer my right hand. A couple of years ago I decided that it would be cool to do everything both hands, so I practiced writing with my right, brushing teeth with my left and stuff. Now I still prefer left for writing, but sometimes still use my right hand when the pen is on the right side of the sheet or the chalk on the right side of the board, and with most other things it depends on the situation which hand I use. The only thing I really trained to do right-handed even though I started as a lefty was playing guitar, simply because no one has a left-handed guitar. For martial arts, I don't bother which leg is my front leg, but I've got more power in my right one when it comes to kicking. So I really don't know, left, right, whatever..
I'm a creative lefty (I love drawing) and I also love martial arts. I'm not going to say I'm really good at it because I'm not even close to a fraction of as good as I want to be (Also I'd just get spammed for saying it). However, I do not believe that's because I'm lefy handed (although because people aren't usually used to fighting lefties so that might help). If you're talking about creativity in martial arts. Then you could be right. But it wouldn't apply to all lefties.
This is cross dominance, which as it would happen is my situation. (For example, I write better left handed but I draw and paint the other way round.)
I'm mainly right-handed, but I'm left handed for a few things. I'm definately not ambi-dextrous, because what I do best with my right I'm lousy at with my left, and vice-versa. I am quite two-footed though.