ma·tri·ar·chy 
(mātrē-är′kē)
(mātrē-är′kē)n. pl. ma·tri·ar·chies
1.
a. A social system in which the mother is head of the family.
b. A family, community, or society based on this system or governed by women.
2. The collection of women in positions of power, especially in such a social system or community. In all senses also called matriarchate.