Let "V" and "W" be vector spaces over a field (or more generally, modules over a ring) and let "T" be a linear map from "V" to "W". If 0"W" is the zero vector of "W", then the kernel of "T" is the preimage of the zero subspace {0"W"}; that is, the subset of "V" consisting of all those elements of "V" that are mapped by "T" to the element 0"W". The kernel is usually denoted as , or some variation thereof: