Generalizations of the Singular Value and QR-Decompositions
- 1 October 1992
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 13 (4) , 993-1014
- https://doi.org/10.1137/0613060
Abstract
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.Keywords
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