28 - Kernel

Kernel / Null Space

Let $V,W$ be vector spaces
Let $T:V\to W$ be linear

$$\ker T:=\{v\in V\mid T(v)=0_W\}$$

In other words, $\ker T$ contains vectors that are sent to $0_W$ by the map $T$

Nullity

Let $V,W$ be vector spaces with $V$ finite-dimensional
Let $T:V\to W$ be linear

$$\mathrm{nullity}(T):=\dim (\ker T)$$