Looks to be spot on! It's extremely interesting that one of the key elements is the *quadratic extension* of the base field. This makes some sense, as the singular values are *square roots* of the eigenvalues. Interesting: posted Jan 6, 2019 -- although first version was posted May, 2018. It's possible that the last time I searched for this particular combination was prior to May, 2018, so I would have missed this paper. At 05:27 PM 2/21/2019, Victor Miller wrote:

Look here: https://arxiv.org/pdf/1805.06999.pdf

On Thu, Feb 21, 2019 at 20:06 Henry Baker <hbaker1@pipeline.com> wrote:

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Hi Gene:

Over the past several years, I've probably downloaded north of 1,000 papers on this subject, but I still haven't found any that address this direct question:

"So you've heard all this cool stuff about matrix factorization (eigenvalue decomp, SVD, polar decomp, etc.) over the reals & complex numbers; what happens to all of this stuff when you move over to the Galois fields?"

There are huge numbers of papers about aspects of linear algebra over Galois fields in coding theory, which is all interesting, but -- so far as I know -- these traditional matrix decomps aren't used in coding theory (are they?).

At 04:27 PM 2/21/2019, Eugene Salamin via math-fun wrote:

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Lots of Google hits for linear algebra over finite fields, as well as p-adic linear algebra.