Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cayley Hamilton theorem with sandwich coefficients for n$\times$n
  matrices over a ring satisfying [x,y][u,v]=0   If A is an n \times n matrix over a ring R satisfying the polynomial identity
[x,y][u,v]=0, then an invariant Cayley-Hamilton identity of the form
  \Sigma A^{i}c_{i,j}A^{j}=0 with c_{i,j}\in R and c_{n,n}=(n!)^2 holds for A.

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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: stat