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If I learnt anything from writing my own software rendered 3D engine it's that matrices are just a way to encode a bunch of vector operations. You don't even have to use them. You can just do these operations directly. But it's a nice way to compactly represent them.

That's what I ended up doing ! Matrices are just too alien to me since I got no formal education in math or programming. On the other hand I've been using vectors constantly in gamedev. But most resources about graphics programming take for principle that you understand them...

I think of them as an operation provided by some weird hardware you have to interface with. You know how some hardware provides you an operation that does A+B*X in one instruction? (You just have to specify A, B, and X). Each row of the matrix describes how to modify each component of your vector.