The QRD and SVD of matrices over a real algebra

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• 作者：Paul Ginzberg ; ^{paul.ginzberg05@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Christiana Mavroyiakoumou ^{christiana.mavroyiakoumou13@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A33 ; 15A18 ; 15A66 ; 16S34 ; 16S35 ; 65F25 ; 65F30
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：504
• 期：Complete
• 页码：27-47
• 全文大小：712 K

文摘

Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD to a wide class of real algebras, including all finite-dimensional semi-simple algebras, (twisted) group algebras and Clifford algebras. Two approaches are described for computing the QRD/SVD: one Jacobi method with a generalised Givens rotation, and one based on the Artin–Wedderburn theorem.