sentences:  For a matrix "A", the column space, row space, null space, and left null space are sometimes referred to as the "four fundamental subspaces".Similarly the column space (sometimes disambiguated as "right" column space) can be defined for matrices over a ring "K" as
  for any "c"1, ..., "cn", with replacement of the vector "m"-space with "right free module", which changes the order of scalar multiplication of the vector v"k" to the scalar "ck" such that it is written in an unusual order "vector"–"scalar".Let "K" be a field of scalars.