The QRD and SVD of matrices over a real algebra
Rings and Algebras
2015-12-08 v1
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.
Keywords
Cite
@article{arxiv.1512.02121,
title = {The QRD and SVD of matrices over a real algebra},
author = {Paul Ginzberg and Christiana Mavroyiakoumou},
journal= {arXiv preprint arXiv:1512.02121},
year = {2015}
}
Comments
Uses elsarticle.cls