I was reading an old linear algebra textbook today, and I was actually having some trouble understanding the notation given in a problem. Here is what it said (or something similar): Consider the $n \times n$-matrix $Q$ given by $Q=(Q_{i,j})_{i,j=1,\ldots,n}$ with $Q_{i,j}=\sin (j/(\cos i + \sin j))$
If $n$ were $4$ or $5$ let's say, what would this matrix look like? The notation first given for $Q$ is throwing me off.
The first part $Q = (Q_{ij})$ is saying that the entry in the $i$th row and $j$th column of $Q$ is the number $Q_{i,j}$. And $i,j = 1, \ldots,n$ is saying that both $i$ and $j$ each range from 1 to $n$ so your matrix $Q$ is $n \times n$. The formula for that entry $Q_{i,j}$ is given by the second equation you cited. Not sure how to further explain that part...