Columns property
= Columns property
If $c_1,\ldots,c_n$ are the columns of a matrix, the matrix has the columns property when $[n]$ has an ordered partition $B_1\sqcup\cdots\sqcup B_s$ such that
$$
\sum_{i\in B_1}c_i=0
$$
and, for $j>1$, $\sum_{i\in B_j}c_i$ belongs to the <linear span> of the columns indexed by $B_1\cup\cdots\cup B_{j-1}$.
= Columns condition
{synonym}