The Collaborative International Dictionary of English v.0.48:

Matriarchate \Ma"tri*ar"chate\, n.
   The office or jurisdiction of a matriarch; a matriarchal form
   of government.
   [1913 Webster]

WordNet (r) 3.0 (2006):

matriarchate
    n 1: a form of social organization in which a female is the
         family head and title is traced through the female line
         [syn: matriarchy, matriarchate]