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.

  • 1
    $\begingroup$ 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
  • 2
    $\begingroup$ 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

It refers to taking the maximum over all the $i$'s, so $$\mu=\max(-q_{11},-q_{22},-q_{33})=\max(3,2,1)=3.$$

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.