Brenier’s theorem unifies polar factorization and Helmholtz decomposition
docmilanfar · x · 2026-07-22
The thread introduces Brenier’s theorem as a unifying result behind several familiar decompositions.
- It asks what polar coordinates, polar matrix factorization, and Helmholtz decomposition have in common.
- The answer given is Brenier’s theorem, a cornerstone of optimal transport.
- The author argues the result is foundational but not widely known, and uses it as the starting point for the rest of the thread.
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