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Post Closed as "Not suitable for this site" by Johannes Hahn, user6976, David Handelman, Chris Godsil, Ben McKay
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edit approved Mar 30, 2018 at 13:03
Rodrigo de Azevedo
edit approved Mar 30, 2018 at 13:03
Rodrigo de Azevedo
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For any nonnegative semidefinite matrix $A$ and any matrix $B$, do we have $$ tr(AB) \le tr(A) \|B\| $$ where

$$\mbox{tr} (AB) \le \mbox{tr} (A) \, \|B\|$$

where $tr(\cdot)$$\mbox{tr}(\cdot)$ is the trace and $\|\cdot\|$ is the operator norm. How to prove this?

For any nonnegative semidefinite matrix $A$ and any matrix $B$, do we have $$ tr(AB) \le tr(A) \|B\| $$ where $tr(\cdot)$ is the trace and $\|\cdot\|$ is the operator norm. How to prove this?

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 to prove this?

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Ivanov
Ivanov
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Matrix trace & norm

For any nonnegative semidefinite matrix $A$ and any matrix $B$, do we have $$ tr(AB) \le tr(A) \|B\| $$ where $tr(\cdot)$ is the trace and $\|\cdot\|$ is the operator norm. How to prove this?