Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-identities on matrices and the Cayley-Hamilton polynomial   We consider certain functional identities on the matrix algebra $M_n$ that
are defined similarly as the trace identities, except that the "coefficients"
are arbitrary polynomials, not necessarily those expressible by the traces. The
main issue is the question of whether such an identity is a consequence of the
Cayley-Hamilton identity. We show that the answer is affirmative in several
special cases, and, moreover, for every such an identity $P$ and every central
polynomial $c$ with zero constant term there exists $m\in\mathbb{N}$ such that
the affirmative answer holds for $c^mP$. In general, however, the answer is
negative. We prove that there exist antisymmetric identities that do not follow
from the Cayley-Hamilton identity, and give a complete description of a certain
family of such identities.

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The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga