Factory Reset: Gmail Acct linked to Market Apps?

[GHII]

I've searched through factory reset threads, but none mention what I am looking for. I was just wondering about purchased apps or even free apps, are they linked to your gmail account? If I do a factory reset, and sign back in, will they show up as purchased? I will probably make a list of Apps I want to re-download before I reset, but I was just checking everything I would need to backup before i do it...

(and for anyone wondering, my phone is just getting sluggish and slow lately, resetting by itself and locking up...I've download and delete more apps than I can remember, and I just want to start from scratch again and get rid of any loose files there might be)

[Backnblack]

The paid apps will show up in the market on your downloads as long as you sign up with the same account. The free apps you will have to redownload unless you back them up with something like astro...