1 #definition null space, kernel, \(\text{null }T\) def
For \(T \in \mathcal L(V, W)\), the null space of \(T\), denoted \(\text{null }T\), is the subset of \(V\) consisting of those vectors that \(T\) maps to 0: \[ \text{null }T = \{v \in V : Tv = 0\} \]