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In addition to the main package {\sc CLIFFORD}, in Sections \ref{sec:svd1} and \ref{sec:svd2} we have used the following additional procedures from a supplementary package {\sc avsd}.
\begin{itemize}
\item Procedure {\tt phi} provides an isomorphism between a matrix algebra and a Clifford algebra.
\item Procedure {\tt radsimplify} simplifies radical expressions in matrices and vectors.
\item Procedure {\tt assignL} is needed to write output from a Maple procedure {\tt eigenvects} in a suitable form, it sorts eigenvectors according to the corresponding eigenvalues, and it uses the Gram-Schmidt orthogonalization process, if necessary, to return a complete list of orthogonal eigenvectors.
\item Procedure {\tt climinpoly} belongs to the main package {\sc CLIFFORD}. It computes a minimal polynomial of any element of a Clifford algebra.
\item Procedure {\tt makediag} makes a ``diagonal" $\Sigma$ matrix consisting of singular values.
\item Procedure {\tt embed} embeds the given non-square matrix or a matrix of smaller dimensions into a $2^k \times 2^k$ matrix of smallest $k$ such that it can be mapped into a Clifford algebra.
\end{itemize}
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