CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article may require cleanup to meet Wikipedia's quality standards . The specific problem is: Remove redundancies. Clean up markup. Do something with short sections . Please help improve this article if you can. (September 2013) In linear algebra and functional analysis , the kernel (also null space or nullspace ) of a linear map L : V → W between two vector spaces V and W , is the set of all elements v of V for which L ( v ) = 0 , where 0 denotes the zero vector in W . That is, in set-builder notation , 1 Properties of the Kernel 2 Application to modules 3 The kernel in functional analysis 4 Representation as matrix multiplication 4.1 Subspace properties 4.2 The Row Space of a Matrix 4.3 Left null space 4.4 Nonhomogeneous systems of linear equations 5 Illu...