You're conflating the implementation with the principle. There is no matrix math with neurons; quite the opposite, we posit the existence of the matrix math from the behavior we've observed with neural systems governed by a sigmoid function. The equations we've derived are secondary to the initial implementation. Just as you tweak the error factor in backprop, so too do weights between intersecting neuron networks adjust until thought and intention falls into line with eventual perception and execution.

The map is not the territory.