Better Notation for Matrices

Let $[l]:=\{1,\dots ,l\}$.

Given an $r\times c$ matrix $M$, let $M^i$ denote the ith column, with $i\in [c]$, and $M_j$ denote the jth row, with $j\in [r]$ and $M_j^i$ denotes a single entry. This makes it alot easier to swap between transposes when doing calculations. For example, if ${\Delta }_i$ is a vector of bits, with $\cdot$ denoting multiplication, and $\ast$ denoting convolution, you can do:

$$\begin{array}{rl}& M^i=T^i+{\Delta }_i\cdot X^i\\ & M_j^i=T_j^i+{\Delta }_i\cdot X_j^i\\ & M_j=T_j+\Delta \ast X_j\end{array}$$

This is a lot more convenient.

The only issue is that this conflicts with tensor notation. Thankfully, there’s not much overlap between general relativity and Cryptography.