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Reference.org
Polar factorization theorem
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<p>In <a href="/facts/Transportation_theory_(mathematics)/DRoHNtde">optimal transport</a>, a branch of mathematics, polar factorization of vector fields is a basic result due to Brenier (1987), with antecedents of Knott-Smith (1984) and Rachev (1985), that generalizes many existing results among which are the <a href="/facts/Polar_decomposition/XWQLdp9B">polar decomposition</a> of real matrices, and the rearrangement of real-valued functions. </p>