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arXiv · 1512.02121

The QRD and SVD of matrices over a real algebra

Paul Ginzberg·Christiana Mavroyiakoumou
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Abstract

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.

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Paul Ginzberg, Christiana Mavroyiakoumou. 2015-12-07. The QRD and SVD of matrices over a real algebra. https://arxiv.org/abs/1512.02121

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