How was the singular value decomposition originally derived? How might one discover this decomposition from first principles?

Question

How was the singular value decomposition (SVD) method originally derived? How might one discover decomposition this from first principles?

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Related Q&As that lend intuition to SVD but not derive or show how one might come up with such a decomposition:

1. Understanding the singular value decomposition (SVD)
2. What is the intuition behind SVD? (cross validated stack exchange)