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In mathematics, especially algebraic geometry the decomposition theorem is a set of results concerning the cohomology of algebraic varieties.

2 votes

Is there an elementary proof of the polar factorization theorem for vector-valued function?

Here's an elementary type argument I learned, based on unique splitting $T=S+A$ of linear operators $T: \mathbb{R}^n \to \mathbb{R}^n$. (i) every linear operator $T$ can be uniquely decomposed $T=S+A$ …
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