## Unit1.2.3A convention regarding the letters used for the loop index

When we talk about loops for matrix-matrix multiplication, it helps to keep in mind the picture

which illustrates which loop index (variable name) is used for what row or column of the matrices.

• Index $i$ is used to index the row of $C$ and corresponding row of $A \text{.}$

• Index $j$ is used to index the column of $C$ and corresponding column of $B \text{.}$

• Index $p$ is used to index the column of $A$ and corresponding row of $B \text{.}$

We try to be consistent in this use, as should you.

###### Remark1.2.4.

In the literature, people often use $i\text{,}$ $j\text{,}$ and $k$ for indexing the three loops and talk about the $ijk$ loop ordering when we talk about the IJP ordering (later in Week 1). The problem with that convention is that $k$ is also used for the "inner size" of the matrices (the column size of $A$ and the row size of $B$). It is for this reason that we use $p$ instead.

Our convention comes with its own problems, since $p$ is often used to indicate the number of processors involved in a computation. No convention is perfect!