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Polar decompositions of quaternion matrices with respect to a givenindefinite inner product are studied. Necessary and sufficient conditions forthe existence of an $H$-polar decomposition are found. In the process anequivalent to Witt's theorem on extending $H$-isometries to $H$-unitarymatrices is given for quaternion matrices.

Polar decompositions of quaternion matrices in indefinite inner product spaces