For real $A\in\mathbb R^{m\times n}$, the left null space is $\ker A^T=\{y:y^TA=0\}\subseteq\mathbb R^m$. For complex inner-product geometry, use $\ker A^*$ and $y^*A=0$. It consists of vectors orthogonal to all columns and has dimension $m-\operatorname{rank}A$.
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