The Kernel and the Range

Note

Let $T:{\mathbb{R}}^n\to {\mathbb{R}}^m$ be a linear transformation. The kernel of T is

Ker(T) = $\{\vec{x}\in {\mathbb{R}}^n\mid T(\vec{x})=\vec{0}\}$

Kernel is also sometimes known as the nullspace

Note

Let $T:{\mathbb{R}}^n\to {\mathbb{R}}^m$ be a linear transformation. The range of T is

Range(T) = $\{T(\vec{x})\mid \vec{x}\in {\mathbb{R}}^n\}$