Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On pseudo-invereses of matrices and their characteristic polynomials in
  supertropical algebra   The only invertible matrices in tropical algebra are diagonal matrices,
permutation matrices and their products. However, the pseudo-inverse
$A^\nabla$, defined as $\frac{adj(A)}{det(A)}$, with $det(A)$ being the
tropical permanent (also called the tropical determinant) of a matrix $A$,
inherits some classical algebraic properties and has some surprising new ones.
Defining $B$ and $B'$ to be tropically similar if $B' =A^\nabla BA$, we examine
the characteristic (max-)polynomials of tropically similar matrices as well as
those of pseudo-inverses. Other miscellaneous results include a new proof of
the identity for $det(AB)$ and a connection to stabilization of the powers of
definite matrices.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph