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arXiv · 2106.10527

Polar decompositions of quaternion matrices in indefinite inner product spaces

G. J. Groenewald·D. B. Janse van Rensburg·A. C. M. Ran·F. Theron·M. van Straaten
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Abstract

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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G. J. Groenewald, D. B. Janse van Rensburg, A. C. M. Ran, F. Theron, M. van Straaten. 2021-06-19. Polar decompositions of quaternion matrices in indefinite inner product spaces. https://arxiv.org/abs/2106.10527

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