Matrix Kernels

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map

$$L : V \rightarrow W$$ between two vector spaces $V$ and $W$, the kernel of

$L$ is the vector space of all elements $v$ of $V$ such that $L(v) = 0$, where 0 denotes the zero vector in $W, or more symbolically:

$$ker(L) = \{ v \in V \hspace1ex | \hspace1ex L(v) = 0\} = L^{-1}(0)$$.