9

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.

Stefan Hansen
  • 25,582
  • 7
  • 59
  • 91
EGSMIB
  • 93
  • 1
  • 3
  • 1
    If you found the answer to be correct and helpful, you might want to accept it by clicking the "Right" sign besides the answer. :-) –  Dec 06 '12 at 08:30
  • 3
    If the maximum refers to the specific value of $i$ that gives the maximum value, then $\arg\max$ is often used (see this). – Stefan Hansen Dec 06 '12 at 08:36

1 Answers1

13

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