Left null space
= Left null space
{title2=$\ker A^T$}
For a real <matrix> $A$, its <left null space> consists of the <vectors> $w$ with $w^TA=0$, or equivalently $A^Tw=0$. It is the <null space> of the <matrix transpose>, and is the <orthogonal complement> of the <column space>. The <linear system> $Ax=b$ is solvable exactly when $w^Tb=0$ for every such $w$.