I have a fair amount on them in KY and TN and some in MO. I checked my records of the 1850 census for Hamilton's parents, and this is the correct family. Thomas and Elizabeth (first cousins, apparently), who are listed on the same page with much of their family, were Hamilton's parents, and Martha Mathis (husband James Mathis listed on the previous page) was his sister. According to family researchers, James Mathis and Martha Jane Mathis were siblings. James Alexander, whose family is also listed on the same page, was Thomas's brother.
What are your ties to the family. I can't completely sort it out, but my ancestor is either Thomas's brother or his first cousin through both fathers and mothers.
E-mail me, and we can exchange more information; however, I'll be tied up with my nephew's wedding for the next few days.