The [[Linear Subspace]] in whose [[Image]] through a [[Matrix Product]] with $A$ is $\vec 0$. $\huge \begin{align} A &\in M_{n\times n} \\ \op{Nul}(A) &= \set{\vec x \in \R^m \mid A\vec x = \vec 0} \end{align} $ The [[Nullspace]] of a [[Matrix]] is equal to the [[Reduced Row Echelon Form]] of said [[Matrix]]. $\huge \op{Nul}(A) = \op{Nul}(\op{rref}(A)) $ $\huge \begin{align} \op{rref}(A) &= E_{1} E_{2} \cdots E_{k} A \\ A\vec x = 0 &\rightarrow\, E_{1} E_{2} \cdots E_{k} A \vec b = 0 \end{align}$ When describing a [[Matrix]] as a [[Linear Transformation]], the [[Nullspace]] is called the [[02 Areas/Math/Kernel|Kernel]].