Kernel of a linear transformation

$$\text{Ker}(L)=\{\vec{x}\in {\mathbb{R}}^n|L(\vec{x})=\vec{0}\}$$

The set of all vectors that land on the origin after going through the transformation.

• $\text{Ker}(L)$ is a subset of Rn cuz these xs belong in Rn.

Translating this to matrix-ish notation:

• We can see that the kernel is same as the nullspace of $[L]$.
  • Null space refers to the set of vectors that land on origin after the matrix transformation.
• Hence, the kernel is also a subspace.