Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path methods for strong shift equivalence of positive matrices   In the early 1990's, Kim and Roush developed path methods for establishing
strong shift equivalence (SSE) of positive matrices over a dense subring U of
the real numbers R. This paper gives a detailed, unified and generalized
presentation of these path methods. New arguments which address arbitrary dense
subrings U of R are used to show that for any dense subring U of R, positive
matrices over U which have just one nonzero eigenvalue and which are strong
shift equivalent over U must be strong shift equivalent over U_+. In addition,
we show positive real matrices on a path of shift equivalent positive real
matrices are SSE over R_+; positive rational matrices which are SSE over R_+
must be SSE over Q_+; and for any dense subring U of R, within the set of
positive matrices over U which are conjugate over U to a given matrix, there
are only finitely many SSE-U_+ classes.

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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex