I am having trouble figuring this out. Any help would be appreciated.
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1 Answer
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Hint: block out $Q$'s rows and $\Sigma$'s columns like this: $$ Q = \left[\begin{array}{c} Q_1^T\\ \vdots \\ Q_n^T \end{array}\right] $$ and $$ \Sigma = \left[\begin{array}{ccc} \Sigma_1 & \cdots & \Sigma_n \end{array}\right]. $$ Then $$ \text{tr}(Q\Sigma) = \sum_{i=1}^n Q_i^T\Sigma_i. $$
Alternative hint 2: use properties of the trace operator (e.g. linearity and cylic property).
Alternative hint 3: Juse do out all the multiplications and use linearity/definitions. It helps to know how to write quadratic forms as a double sum, if you take this approach.
