True or False - The Fall of Sparta and Matriarchy

More recently I have encountered here with a hypothesis - Sparta collapsed because of too much free manners women.
Usually they say about too increased female greed, indifference to other people's lives. They write that "...matriarchal orders rapidly decompose the emerging new economic order, in this case - feudalism (from myself - I can not name Spartan feudal system) and lead to a stupid and selfish eating away its resources, which could encourage social progress Outcome. - regression and degeneration, the decline of the state, the subordination of the patriarchal invaders. "
Is this true, and what do you think about this?
 
Spartan women might have been less restricted than in other Greek states, but I think it's going a bit far to call Sparta a matriarchy. More likely, the decline of Sparta was caused by the helot system and the fact that they always had to devote significant resources to keeping their slave class in check.
 
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