What is thinking if not a series of matrix operations? Your brain is just a huge network of neurons and their connections, is this not a (very complex) matrix?

Certainly not in any mathematical sense. The discrete N-dimensional coefficients of a matrix are not modeled by neurons, their connections, and the quantum mechanical electrical accidents that (a) constitute one's wetware, and (b) aren't completely captured by gates and code.

The map is still not the territory, sorry.