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For questions involving the trace of a square matrix, i.e. the sum of the elements on the main diagonal.
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Matrix trace & norm [closed]
For any nonnegative semidefinite matrix $A$ and any matrix $B$, we have
$$\mbox{tr} (AB) \le \mbox{tr} (A) \, \|B\|$$
where $\mbox{tr}(\cdot)$ is the trace and $\|\cdot\|$ is the operator norm. How …