I am confused by the notations I am seeing in my linear algebra class.
Here is the book I am using and page I am on.
$R_i \leftrightarrow R_j$ means to interchange rows $i$ and $j$ of a matrix.
But does $R_{ij}$ not mean matrix $R$, and that $i$ is the row, and $j$ is the column?
So why do we then refer to $i$ and $j$ in $R_i$ and $R_j$ both as rows now?
Best Answer
$i$ and $j$ are just indices. They don't have any particular meaning on their own. If $R_{ij}$ is used to denote the entry of matrix $R$ in the $i$th row and $j$th column, then $R_{ji}$ would mean the entry in the $j$th row, $i$th column. It's the position of the letter, and not the letter itself, that tells you row vs column.
Now if I were writing a book would I use the notation $R_{ij}$ (with two indices) to mean the $(i,j)$th entry of $R$ and also $R_i$ (with one index) to mean the $i$th row? Probably not, as it seems bound to cause confusion. Is it possible the book you're reading did exactly this? Yes. (Though in the chapter you linked, I only see $R_i$ and not $R_{ij}$.)