Given $(0,1)$ matrix of arbitrary size $\mathbb{R}^{m \times n}$, is there an efficient algorithm to enumerate all combinations that any column is a sum of other columns?
For example:
$$ M=\begin{bmatrix} 1 & 0 & 0 & 0 & 1\\ 0 & 1 & 0 & 1 & 1\\ 0 & 0 & 1 & 1 & 1\\ \end{bmatrix} $$
With $[i]$ representing the $i^{th}$ column, we have three combinations
- $[4] = [2] + [3]$
- $[5] = [1] + [4]$
- $[5] = [1] + [2] + [3]$
Programming in Matlab if that helps.