Null spaces are orthogonal complements of the corresponding row or column spaces

For $A\in\mathbb C^{m\times n}$, $\ker A=(\operatorname{range}A^*)^\perp\subseteq\mathbb C^n$ and $\ker A^*=(\operatorname{Col}A)^\perp\subseteq\mathbb C^m$. Over $\mathbb R$, $\ker A=(\operatorname{Row}A)^\perp$. The original statement confusing the right null space with the complement of the column space had a dimension mismatch.Copy