Nullspace

definitionvector-spaces

Definition

For some $T\in \mathcal{L}(V,W)$, the nullspace of $T$, denoted by $\mathrm{null}T$ (or $\ker T$), is the subset of $V$ given by all vectors that map to $0$ under $T$:

$$\mathrm{null}T=\{v\in V:Tv=0\}.$$

Properties

• For map $T:V\to W$, $\mathrm{null}T$ is a subspace of $V$.

Examples