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This paper discusses multimatrix generalizations of two well-known orthogonal rank factorizations of a matrix: the generalized singular value decomposition and the generalized QR-(or URV-) decomposition. These generalizations can be obtained for any number of matrices of compatible dimensions. This paper discusses in detail the structure of these generalizations and their mutual relations and gives a constructive proof for the generalized QR-decompositions.
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Moor et al. (1992) studied this question.
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