null space

$\operatorname{Nul}(A)$ — every $\mathbf x$ with $A\mathbf x = \mathbf 0$ .

For an $m\times n$ matrix $A$ , the null space $\operatorname{Nul}(A)$ is the set of every $\mathbf x\in\mathbb R^n$ satisfying $A\mathbf x=\mathbf 0$ — exactly the solution set of the homogeneous system. $\operatorname{Nul}(A)$ is always a subspace of $\mathbb R^n$ , since it contains $\mathbf 0$ and is closed under addition and scalar multiplication by linearity of matrix-vector multiplication.