  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.
