Better Notation for Matrices

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

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 $M^i_j$ 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 $*$ denoting convolution, you can do:

$$ \begin{aligned} &M^i = T^i + \Delta_i \cdot X^i \cr &M^i_j = T^i_j + \Delta_i \cdot X^i_j \cr &M_j = T_j + \Delta * X_j \end{aligned} $$

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.