Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consimilarity and quaternion matrix equations $AX-\hat{X}B=C$,
  $X-A\hat{X}B=C$   L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a
quaternion matrix $A$ with respect to consimilarity transformations
$\tilde{S}^{-1}AS$ in which $S$ is a nonsingular quaternion matrix and
$\tilde{h}:=a-bi+cj-dk$ for each quaternion $h=a+bi+cj+dk$. We give an
analogous canonical form of a quaternion matrix with respect to consimilarity
transformations $\hat{S}^{-1}AS$ in which $h\mapsto\hat{h}$ is an arbitrary
involutive automorphism of the skew field of quaternions. We apply the obtained
canonical form to the quaternion matrix equations $AX-\hat{X}B=C$ and
$X-A\hat{X}B=C$.

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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga