Nope it's not the Same Mathis, the Mathis Arabella killed was Cassius's Father. The Mathis that drove Henry from the mainland is still there.
However there is also abit of back groundy stuff in the Karogar information when i explain how Lar's is related to Henry and Vince Bendett.
In short.
Mathis and Vince Bendett's Father (one of his knights) Invaded Lar's homeland.
Both men, bedded and had a relationship with native women during thier trip (two sister's infact)
While Vince's father bought his new lady friend home and married her (producing vince). Mathis left leaving his illigitamate child behind (Lars).
In short this makes Lar's Henry's nephew and as Mathis's firstborn he has some rights over the throne of the mainland. However as an illegitamate child he would struggle to claim it.
As for the name of the Mainland... i don't think i ever bothered to name it i supose i should. haha.