Ok, they can't wear armor. I assume that is for balance reasons. So they can still benefit from mage armor, right? What about bracers of armor?
If you magically force an eidolon to don armor, does it become unsummoned?
It's pretty much impossible to magically force an Eidolon to do anything its Summoner doesn't want it to do.
Yes, you can still cast mage armor on them. If they have the Limbs (Arms) evolution and the Summoner isn't wearing any bracers, they can also wear bracers of armor.
