Upvoted for your precision and accuracy in pointing out the distinction between the words matriarchal and matrilineal. A matriarchal society would be one where women dominated in political power. My short Internet search did not turn up any societies I would call both matriarchal (instead of matrilineal) and likely to be real, so I assume they are either extremely rare or nonexistent. A matrilineal society such as the one in the study is one that traces its ancestry through the female line--this trait does not mean that females have political power in the culture. I would add that matrilineal societies may also tend to differ from patrilineal socities in that women may have greater access to resources within the family, such as family earnings and inheritances. This does not make the society matriarchal since men still occupy the positions of political power.

Sidenotes:

• The Wikipedia article on matriarchy I linked to presently asserts that "There are no known societies that are unambiguously matriarchal" with six references to this statement. Contradictions to this statement exist in the article, but from what I read they are not as well supported (at least not the ones I saw--I did not read the entire article). Hence why the Wikipedia article seems to me to support the likely rareness or nonexistence of matriarchal cultures. And yes, I do give some amount of credence to Wikipedia, even with all its flaws.

• The second link I include about the Mosuo culture living in China seems to be matrilineal rather than matriarchal as supported by this statement in the article: "Political power in Mosuo society tends to be in the hands of males, which for many scientists disqualifies them as a true matriarchy, and they would be rather called "matrilineal"."

• The matrilineal Nagovisi of the third link I included are interesting in that they are also described as having "anarchistic tendencies", and so do not seem to have a strong central political structure dominating their society. Also, gardening is said to be very important to them and the garden is a pivotal resource around which their culture revolves. As a sidenote to my sidenote, their country of origin, Papua New Guinea, is, in the words of the CIA World Factbook, "one of the most [culturally] heterogeneous in the world; PNG has several thousand separate communities, most with only a few hundred people...".