Any kind of book recs would be awesome! I want to make this world as detailed and layered as possible -- I don't want the society to be exactly like normal, but with a lady in charge. If women had been at the wheel since the dawn of this civilization, there would doubtless be some huge differences. So yeah, if there's any kind of book that has that element, I'd be super interested.
I'll definitely PM you when I have more concrete questions.
A Brother's Price -- This is a romance in a lot of ways, but is really good.
God's War -- This one is awesome, and should be better-known.
The Labyrinth series by Pearl North -- This reads like YA, which is hurting my head, so I haven't actually gotten to the damn matriarchy description yet. Apparently they go more in-depth in the second book about that society.
Carnival by Elizabeth Bear -- This is on my TBR list, but definitely features a matriarchy. No idea how good it is.
Amberlight -- This just came up when I was googling looking for the titles of the other matriarchy books I've read and can't currently recall the names of. So no idea if it's any good, but it has a matriarchy.
There are some other older ones I've read, but they were truly horrible, so I'm not going to list them, lol. There are a couple more good ones, but I guess I'll have to wait until my family's awake and I can get to the rest of my books to look at their titles.
ETA: I second what others have said about typing "matriarchy" into Wikipedia and reading what comes up. They had some interesting descriptions of theoretical matriarchies, IIRC.
My problem with researching this has always been that, after reading for about 10 minutes, I throw the source across the room and shout "the Greek Amazons were more interesting!". I'm too personally obsessed with that myth to pay much attention to other inspirations, lol.