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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†Department of Mathematics and Applied Mathematics, Research Focus: Pure and Applied Analytics, North-West University, Private Bag X6001, Potchefstroom 2520, South Africa (email@example.com, firstname.lastname@example.org, email@example.com, firstname.lastname@example.org). Supported by a grant from DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).
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- Extending isometries
- H-polar decompositions
- Indefinite inner product
- Quaternion matrices
- Square roots of matrices
- Witt’s theorem