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}


Columns property

{title2=$\operatorname{span}(S)$}
{wiki}

The linear span of a subset $S$ of a <vector space> is the set of all finite <linear combination>[linear combinations] of elements of $S$.


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 Incoming links: Linear span