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> matrices can approximate any function

I'm not sure what point you're trying to make. Matrices only perform linear transformations, so matrices only approximate functions linearly, which in general, is a terrible approximation globally.

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Especially, if you have complex systems where discretization and linearization aren't computationally achievable and/or numerically accurate ... like predicting global weather patterns or even very small experiments. I think about the phrase: All models are wrong; some models are useful.

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