Math 6420 • PDE

\begin{enumerate}
\item[(a)] State the Singular Value Decomposition Theorem.
\item[(b)] For any \(n\times m\) real matrices \(A\) and \(B\), show the
\(\operatorname{Tr}(AB^*)=\operatorname{Tr}(BA^*)\).
\item[(c)] Show that \(\lVert A\rVert=\sqrt{\operatorname{Tr}(AA^*)}\) is a norm.
\item[(d)] Suppose \(A\) and \(B\) are \(n\times m\) real matrices. Find the orthogonal matrix
\(Q\) that minimizes \(\lVert QA-B\rVert\) using the norm of part c.
\end{enumerate}