The left null space of a matrix is a subspace of R^m (or C^m).

For real $A\in\mathbb R^{m\times n}$, the left null space is $\ker A^T\subseteq\mathbb R^m$; for complex Hermitian geometry use $\ker A^*\subseteq\mathbb C^m$. Each is a subspace because it is a kernel. The latter is $(\operatorname{Col}A)^\perp$, and its dimension is $m-\operatorname{rank}A$.

If one instead defines a complex algebraic left annihilator as rows $zA=0$, specify this convention and convert row/column conjugation consistently.Copy