Kernel

$\text{ker}(T)=\mathcal{N}(\mathbf{A})=\{\vec{x}\in {\mathbb{R}}^m:T(\vec{x})=\vec{0}\}$

• $T:{\mathbb{R}}^m\to {\mathbb{R}}^n$
• Can be thought of as the zeroes of a polynomial function
• $\text{im}(T)\subseteq {\mathbb{R}}^n$ and $\text{ker(T)}$ is a subspace of ${\mathbb{R}}^m$
• Also called the null space of $A$, where $A$ is a matrix of column vectors representing $T$