Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduction of a pair of skew-symmetric matrices to its canonical form
  under congruence   Let $(A,B)$ be a pair of skew-symmetric matrices over a field of
characteristic not 2. Its regularization decomposition is a direct sum \[
(\underline{\underline A},\underline{\underline B})\oplus
(A_1,B_1)\oplus\dots\oplus(A_t,B_t) \] that is congruent to $(A,B)$, in which
$(\underline{\underline A},\underline{\underline B})$ is a pair of nonsingular
matrices and $(A_1,B_1),$ $\dots,$ $(A_t,B_t)$ are singular indecomposable
canonical pairs of skew-symmetric matrices under congruence. We give an
algorithm that constructs a regularization decomposition. We also give a
constructive proof of the known canonical form of $(A,B)$ under congruence over
an algebraically closed field of characteristic not 2.

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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: econ
1
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: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org