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My question is concerning a maximum notation.

I have a $3\times 3$ matrix: $$Q=\begin{bmatrix}-3&2&1\\1&-2&1\\0&1&-1\end{bmatrix},$$

where $q_{ii}$ = $-\sum_{i \neq j} q_{ij}$. Let $\mu = \max_i(-q_{ii})$.

I am unsure what the maximum refers to, having a subscript $i$. Whether it is the value of $i$ that gives the maximum value (in this case that would be $\max(1,1) = 1$, because the maximum value is found at entry $(1,1)$ in the matrix, or if it is the maximum value of $-q_{ii}$ (which in this case is $-(-3) = 3$.)

Any help would be appreciated.

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    $\begingroup$ If you found the answer to be correct and helpful, you might want to accept it by clicking the "Right" sign besides the answer. :-) $\endgroup$ – user14082 Dec 6 '12 at 8:30
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    $\begingroup$ If the maximum refers to the specific value of $i$ that gives the maximum value, then $\arg\max$ is often used (see this). $\endgroup$ – Stefan Hansen Dec 6 '12 at 8:36
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It refers to taking the maximum over all the $i$'s, so $$\mu=\max(-q_{11},-q_{22},-q_{33})=\max(3,2,1)=3.$$

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  • $\begingroup$ Thank you. That helped a lot. $\endgroup$ – EGSMIB Dec 6 '12 at 8:15

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