I tend to agree with vulcan on the "size of the purse" issue for at least 2 reasons:
(1) there are many purses which look just like a backpack (with straps and all). just because someone calls their bag a "purse" does that make it acceptable to carry-on regardless of size?
(2) there are many purses which rival the maximum size of carry-on luggage. I just went over to ebags and saw several which were 16" x 12" x 5".

just food for thought...