An actual matriarchal society is one where political and economic power is vested in women - both in family structures and in culture/society at large. Under this definitiion, there have been very few, if any, real matriarchies. Matrilineal societies are those in which descent and property inheritance is traced through the female line. Most matrilineal societies are in actual practice patriarchical in that the mothers' brothers tended to possess the real power. To imagine a true matriarchy, it is helpful to imagine it's exact opposite: In this definitin a matriarchy would be a society in which men have no decision making authority whatsoever, that they cannot own property and divorce their wives but the wives can divorce them on a whim and are the legal owners of any property they possess, where there are numerous cultural, religious, and legal prohibitions on what men can do apart from their wives, where it is socially accepted for women to have multiple husbands or male lovers but men are harshly punished for any sexual impropriety, where a single man is considered imperfect and somehow sinful, and where men are considered a weaker sex in need of special protection, including restricted access to normal rights excercised by women. There has been no such thing in human history.