Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polar decompositions of quaternion matrices in indefinite inner product
  spaces   Polar decompositions of quaternion matrices with respect to a given
indefinite inner product are studied. Necessary and sufficient conditions for
the existence of an $H$-polar decomposition are found. In the process an
equivalent to Witt's theorem on extending $H$-isometries to $H$-unitary
matrices is given for quaternion matrices.

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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th