Talk:Generalized singular value decomposition

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It seems to me that Q (in the GSVD of A,B) is not generally unitary, and it looks rather obvious that solution where U,V and Q are all simultaneously unitary does not exist. Unitary matrix on the other hand is orthogonal as far as I understand. This is also mentioned in Alter et al. PNAS 2003 100(6)3351 (http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=152296) where they mention that X^-1 (which corresponds to Q on the wiki page) is 'in general nonorthogonal'. I have not time to check this further right now. However, there seems to be some reason for caution.