Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On commuting matrices and exponentials   Let A and B be matrices of M_n(C). We show that if exp(A)^k
exp(B)^l=exp(kA+lB) for all integers k and l, then AB=BA. We also show that if
exp(A)^k exp(B)=exp(B)exp(A)^k=exp(kA+B)$ for every positive integer k, then
the pair (A,B) has property L of Motzkin and Taussky. As a consequence, if G is
a subgroup of (M_n(C),+) and M -> exp(M) is a homomorphism from G to
(GL_n(C),x), then G consists of commuting matrices. If S is a subsemigroup of
(M_n(C),+) and M -> exp(M) is a homomorphism from S to (GL_n(C),x), then the
linear subspace Span(S) of M_n(C) has property L of Motzkin and Taussky.

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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph