Multivariate calculus from first principles
So far the output was a single number. Let it grow into a vector too. A function f: Rⁿ → Rᵐ takes a vector in and returns a vector out: many numbers in, many numbers out. That is the exact shape of a neural-network layer, where an input vector enters and a transformed vector leaves.
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▶ Functions f: Rⁿ → Rᵐ