Factorization of Matrices of Quaternions

Details Factorization of Matrices of Quaternions Factorization of Matrices of Quaternions

2011-07-03

arxiv.org/abs/1107.0500v1

Mathematics

Operator Algebras

20 pages. No figures

Scientific paper

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 ragarding complex matrices that are self-dual or symmetric, but perhaps not Hermitian.

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