  We review known factorization results in quaternion matrices. Specifically,
we derive the Jordan canonical form, polar decomposition, singular value
decomposition, the QR factorization. We prove there is a Schur factorization
for commuting matrices, and from this derive the spectral theorem. We do not
consider algorithms, but do point to some of the numerical literature.
  Rather than work directly with matrices of quaternions, we work with complex
matrices with a specific symmetry based on the dual operation. We discuss
related results regarding complex matrices that are self-dual or symmetric, but
perhaps not Hermitian.
