Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple typical ranks in matrix completion   Low-rank matrix completion addresses the problem of completing a matrix from
a certain set of generic specified entries. Over the complex numbers a matrix
with a given entry pattern can be uniquely completed to a specific rank, called
the generic completion rank. Completions over the reals may generically have
multiple completion ranks, called typical ranks. We demonstrate techniques for
proving that many sets of specified entries have only one typical rank, and
show other families with two typical ranks, specifically focusing on entry sets
represented by circulant graphs. This generalizes the results of Bernstein,
Blekherman, and Sinn. In particular, we provide a complete characterization of
the set of unspecified entries of an $n\times n$ matrix such that $n-1$ is a
typical rank and fully determine the typical ranks for entry set $G(n,1)$ for
$n<9$. Moreover, we study the asymptotic behaviour of typical ranks and present
results regarding unique matrix completions.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th