I was reading a paper and found the following, "$k$-th entry of sorted $S((i,:))$". I don't understand what does this colon notation mean.
Suppose we have $$S=\begin{pmatrix}1.01330\dots &1.00958\dots &0.96263\dots &0.35814\dots &0.75399\dots \\ 0.59616\dots &0.79699\dots &0.56635\dots &0.24665\dots &0.51927\dots \\ 0.32087\dots &0.31970\dots &0.45483\dots &0.11341\dots &0.23876\dots \\ 0.55846\dots &0.70586\dots &0.53054\dots &0.40040\dots &0.52716\dots \\ 0.86933\dots &1.03356\dots &0.82586\dots &0.42076\dots &0.88582\dots \end{pmatrix}$$, then what is the "$k$-th entry of sorted $S((i,:))$"? Can someone explain me?(for exmaple, lets say $k=2$ here.)
By not reading the original passage, I guess $S(i, :)$ is the $i^{\text{th}}$ row of $S$. The colon simply means everyone $-$ in this case every entry from the $i^{\text{th}}$ row. This colon writing is pretty common in MATLAB/Octave. Then the $k^{\text{th}}$ entry of $S(i, :)$ is just $S(i, k)$, the entry at $i^{\text{th}}$ row and $k^{\text{th}}$ column.
In contrast, $S(:, j)$ is the $j^{\text{th}}$ column of $S$.
Edit: If "sorted" just means selecting that row by context, you can skip my edit. But in case "sorted" means some kind of rearranging the entries within that particular row then you need to dump away the $S(i, k)$ stuff and do the rearrangement by yourself. Oscar got me.
E.g. In case you pick the $3^{\text{rd}}$ row: $(0.321\cdots \text{ } 0.320\cdots \text{ } 0.455\cdots \text{ } 0.113\cdots \text{ } 0.239\cdots )$ and the "sorted" means sort the entries in ascending order, then $k = 2$ would pick $0.239\cdots$ instead of $0.320\cdots$.