column space

$\operatorname{Col}(A)$ — the span of a matrix's columns.

Let $A$ be an $m\times n$ matrix with columns $\mathbf a_1,\dots,\mathbf a_n$ . The column space of $A$ , written $\operatorname{Col}(A)$ , is $\operatorname{span}\{\mathbf a_1,\dots,\mathbf a_n\}$ , a subspace of $\mathbb R^m$ — automatically a subspace since span always is. $A\mathbf x=\mathbf b$ is consistent exactly when $\mathbf b\in \operatorname{Col}(A)$ .