On a variational formulation of the generalized singular value decomposition

A variational formulation for the generalized singular value decomposition (GSVD) of a pair of matrices A is an element of R-mxn and B is an element of R-pxn is presented. In particular, a duality theory analogous to that of the SVD provides new understanding of left and right generalized singular vectors. It is shown that the intersection of row spaces of A and B plays a key role in the GSVD duality theory. The main result that characterizes left GSVD vectors involves a generalized singular value deflation process.