Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A dual eigenvector condition for strong lumpability of Markov chains   Necessary and sufficient conditions for identifying strong lumpability in
Markov chains are presented. We show that the states in a lump necessarily
correspond to identical elements in eigenvectors of the dual transition matrix.
If there exist as many dual eigenvectors that respect the necessary condition
as there are lumps in the aggregation, then the condition is also sufficient.
The result is demonstrated with two simple examples.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph