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====== IAM 961 HW2, fall 2015 ====== **Problem 1:** Prove that any real-valued matrix $A$ has a real-valued SVD, i.e. an SVD factorization $A=U \Sigma V^\dagger$ where $U,\Sigma,$ and $V$ are real-valued matrices. **Problem 2:** Show that if $A$ is $m \times n$ and $B$ is $ l \times n$, the product $AB^*$ can be written as \begin{eqnarray*} AB^* = \sum_{j=1}^n a_j b^*_j \end{eqnarray*} where $a_j$ and $b_j$ are the columns of $A$ and $B$. This is more a matter of understanding and proper use of notation than any kind of deep proof! **Problem 3:**