I am wondering how to organise all of those concepts in my head. should i think of it like: subspace > vectorspace > nullspace, columnspace kind of like columnspaces and nullspaces are valid vectorspaces, and all of those are valid subspaces. is a vector space a columnspace? except its definition depends on vectors? also I realised recently that the nullspace of say Ax=0 could be defined in lower dimensions then the columnspace of matrix A. does that mean that those are completely unrelated concepts, except for coming from the same place?