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Assume there exists a new and very efficient algorithm for calculating the polar decomposition of a matrix $A=UP$, where $U$ is a unitary matrix and $P$ is a positive-semidefinite Hermitian matrix. Would there be any interesting applications in Machine Learning? Maybe topic modeling? Or page ranking? I am interested in references to articles and books.

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  • $\begingroup$ Hi and welcome to AI SE! Maybe have a look at geometric deep learning. There are some models there that make use of adjacency matrices and other matrices. $\endgroup$
    – nbro
    May 20, 2020 at 16:25
  • $\begingroup$ Thank you @nbro. Do you have any references I could check out? $\endgroup$
    – Samuel
    May 21, 2020 at 17:04
  • $\begingroup$ Off the top of my head, I don't have a specific reference on GDL that talks about adjacency matrices (because it's been a while since I had to deal with GDL), but I guess that many papers on graph neural networks will talk about it. Maybe ask another question on the site about it. And I (or someone else) will try to provide a more formal answer. $\endgroup$
    – nbro
    May 21, 2020 at 17:11

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