Kernel (linear algebra)

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part (or linear subspace) of the domain which the map maps to the zero vector.^[1] That is, given a linear map L : V → 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,^[2] or more symbolically: $${\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}=L^{-1}(\mathbf {0} ).}$$