The Canonical Generalized Polar Decomposition
SIAM Journal on Matrix Analysis and Applications
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Witt's theorem on the extension of H-isometries to H-unitary matrices with respect to the scalar product generated by a self-adjoint nonsingular matrix H is studied in detail. All possible extensions are given, and their structure as a real analytic manifold is described. Analogous problems with respect to skew-symmetric scalar products are studied as well.The main motivation to study these problems, as well as the main applications of the results obtained, concerns polar decompositions in indefinite scalar product spaces. As another application, for given B all solutions of the matrix equation XA = B with H-unitary X and upper triangular A are described. Equations of this type are of vital importance in hyperbolic QR decompositions.